Division polynomials $\psi_n$ of elliptic curves over $\mathbb{Q}$

$N$

$c_4$, $c_6$

$n$

$\psi_n(x,y)$

11

496, 20008

1:

1

comment: Cremona label 11a1.

11

496, 20008

2:

2*y + 1

comment: Cremona label 11a1.

11

496, 20008

3:

3*x^4 - 4*x^3 - 60*x^2 - 237*x - 21

comment: Cremona label 11a1.

11

496, 20008

4:

4*x^6*y + 2*x^6 - 8*x^5*y - 4*x^5 - 200*x^4*y - 100*x^4 - 1580*x^3*y - 790*x^3 - 420*x^2*y - 210*x^2 - 2992*x*y - 1496*x - 11642*y - 5821

comment: Cremona label 11a1.

11

496, 20008

5:

5*x^12 - 20*x^11 - 604*x^10 - 6705*x^9 + 12015*x^8 + 54960*x^7 + 59145*x^6 + 1460614*x^5 + 6603415*x^4 + 7328555*x^3 - 20139775*x^2 - 45811705*x - 36319600

comment: Cremona label 11a1.

11

375376, 229985128

1:

1

comment: Cremona label 11a2.

11

375376, 229985128

2:

2*y + 1

comment: Cremona label 11a2.

11

375376, 229985128

3:

3*x^4 - 4*x^3 - 46920*x^2 - 3162957*x - 60098081

comment: Cremona label 11a2.

11

375376, 229985128

4:

4*x^6*y + 2*x^6 - 8*x^5*y - 4*x^5 - 156400*x^4*y - 78200*x^4 - 21086380*x^3*y - 10543190*x^3 - 1201961620*x^2*y - 600980810*x^2 - 32498313672*x*y - 16249156836*x - 343309133842*y - 171654566921

comment: Cremona label 11a2.

11

375376, 229985128

5:

5*x^12 - 20*x^11 - 484824*x^10 - 99534705*x^9 - 6120521085*x^8 + 516321783960*x^7 + 125291219129745*x^6 + 11078639692039294*x^5 + 577688788293044015*x^4 + 19209698015743545555*x^3 + 402901490901396589425*x^2 + 4887305810316512472995*x + 26251755532203500725560

comment: Cremona label 11a2.

11

16, -152

1:

1

comment: Cremona label 11a3.

11

16, -152

2:

2*y + 1

comment: Cremona label 11a3.

11

16, -152

3:

3*x^4 - 4*x^3 + 3*x - 1

comment: Cremona label 11a3.

11

16, -152

4:

4*x^6*y + 2*x^6 - 8*x^5*y - 4*x^5 + 20*x^3*y + 10*x^3 - 20*x^2*y - 10*x^2 + 8*x*y + 4*x - 2*y - 1

comment: Cremona label 11a3.

11

16, -152

5:

5*x^12 - 20*x^11 + 16*x^10 + 95*x^9 - 285*x^8 + 360*x^7 - 255*x^6 + 94*x^5 + 15*x^4 - 45*x^3 + 25*x^2 - 5*x

comment: Cremona label 11a3.

14

-215, 5291

1:

1

comment: Cremona label 14a1.

14

-215, 5291

2:

x + 2*y + 1

comment: Cremona label 14a1.

14

-215, 5291

3:

3*x^4 + x^3 + 27*x^2 - 69*x - 26

comment: Cremona label 14a1.

14

-215, 5291

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 46*x^5 + 90*x^4*y - 185*x^4 - 460*x^3*y - 490*x^3 - 520*x^2*y - 79*x^2 + 362*x*y - 582*x - 1526*y - 763

comment: Cremona label 14a1.

14

-215, 5291

5:

5*x^12 + 5*x^11 + 280*x^10 - 2095*x^9 - 3765*x^8 - 8550*x^7 - 40320*x^6 + 66490*x^5 - 341085*x^4 + 292705*x^3 - 182920*x^2 + 867445*x - 386051

comment: Cremona label 14a1.

14

1705, 57707

1:

1

comment: Cremona label 14a2.

14

1705, 57707

2:

x + 2*y + 1

comment: Cremona label 14a2.

14

1705, 57707

3:

3*x^4 + x^3 - 213*x^2 - 837*x - 1330

comment: Cremona label 14a2.

14

1705, 57707

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 354*x^5 - 710*x^4*y - 3145*x^4 - 5580*x^3*y - 16090*x^3 - 26600*x^2*y - 34439*x^2 - 42278*x*y - 4550*x + 33178*y + 16589

comment: Cremona label 14a2.

14

1705, 57707

5:

5*x^12 + 5*x^11 - 2200*x^10 - 27215*x^9 - 152205*x^8 + 474570*x^7 + 12679800*x^6 + 64918930*x^5 + 130981955*x^4 + 276547585*x^3 + 1540586240*x^2 + 4110673005*x + 3643941349

comment: Cremona label 14a2.

14

8185, 742643

1:

1

comment: Cremona label 14a3.

14

8185, 742643

2:

x + 2*y + 1

comment: Cremona label 14a3.

14

8185, 742643

3:

3*x^4 + x^3 - 1023*x^2 - 10485*x - 29944

comment: Cremona label 14a3.

14

8185, 742643

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 1704*x^5 - 3410*x^4*y - 36655*x^4 - 69900*x^3*y - 334390*x^3 - 598880*x^2*y - 1521179*x^2 - 2443478*x*y - 3225860*x - 4008242*y - 2004121

comment: Cremona label 14a3.

14

8185, 742643

5:

5*x^12 + 5*x^11 - 10570*x^10 - 335435*x^9 - 3301395*x^8 + 33058890*x^7 + 1330084140*x^6 + 18055358290*x^5 + 143584984295*x^4 + 721733982865*x^3 + 2227426134350*x^2 + 3726331865625*x + 2368693946359

comment: Cremona label 14a3.

14

25, -253

1:

1

comment: Cremona label 14a4.

14

25, -253

2:

x + 2*y + 1

comment: Cremona label 14a4.

14

25, -253

3:

3*x^4 + x^3 - 3*x^2 + 3*x

comment: Cremona label 14a4.

14

25, -253

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 4*x^5 - 10*x^4*y + 5*x^4 + 20*x^3*y + 10*x^3 + x^2 + 2*x*y - 2*y - 1

comment: Cremona label 14a4.

14

25, -253

5:

5*x^12 + 5*x^11 - 30*x^10 + 85*x^9 + 45*x^8 - 30*x^7 - 50*x^5 + 55*x^4 - 15*x^3 - 10*x^2 + 5*x - 1

comment: Cremona label 14a4.

14

131065, 47449331

1:

1

comment: Cremona label 14a5.

14

131065, 47449331

2:

x + 2*y + 1

comment: Cremona label 14a5.

14

131065, 47449331

3:

3*x^4 + x^3 - 16383*x^2 - 661749*x - 7510776

comment: Cremona label 14a5.

14

131065, 47449331

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 27304*x^5 - 54610*x^4*y - 2233135*x^4 - 4411660*x^3*y - 77313590*x^3 - 150215520*x^2*y - 1287222299*x^2 - 2424229078*x*y - 8852626692*x - 15281024306*y - 7640512153

comment: Cremona label 14a5.

14

131065, 47449331

5:

5*x^12 + 5*x^11 - 169290*x^10 - 21009995*x^9 - 798557715*x^8 + 35462143050*x^7 + 5404417543980*x^6 + 287678453445970*x^5 + 8982520216029415*x^4 + 178546119945167505*x^3 + 2236707043157572430*x^2 + 16198423549734584345*x + 51932734691569837559

comment: Cremona label 14a5.

14

505, -11341

1:

1

comment: Cremona label 14a6.

14

505, -11341

2:

x + 2*y + 1

comment: Cremona label 14a6.

14

505, -11341

3:

3*x^4 + x^3 - 63*x^2 + 147*x - 98

comment: Cremona label 14a6.

14

505, -11341

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 104*x^5 - 210*x^4*y + 385*x^4 + 980*x^3*y - 490*x^3 - 1960*x^2*y - 49*x^2 + 1862*x*y + 588*x - 686*y - 343

comment: Cremona label 14a6.

14

505, -11341

5:

5*x^12 + 5*x^11 - 650*x^10 + 4445*x^9 - 8085*x^8 - 39690*x^7 + 286650*x^6 - 862400*x^5 + 1558935*x^4 - 1812755*x^3 + 1344560*x^2 - 588245*x + 117649

comment: Cremona label 14a6.

15

481, 4879

1:

1

comment: Cremona label 15a1.

15

481, 4879

2:

x + 2*y + 1

comment: Cremona label 15a1.

15

481, 4879

3:

3*x^4 + 5*x^3 - 57*x^2 - 117*x - 139

comment: Cremona label 15a1.

15

481, 4879

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 90*x^5 - 190*x^4*y - 485*x^4 - 780*x^3*y - 1780*x^3 - 2780*x^2*y - 2826*x^2 - 2872*x*y - 316*x + 2240*y + 1120

comment: Cremona label 15a1.

15

481, 4879

5:

5*x^12 + 25*x^11 - 564*x^10 - 4655*x^9 - 23370*x^8 - 40320*x^7 + 265635*x^6 + 1126929*x^5 + 949590*x^4 - 127990*x^3 + 3822190*x^2 + 7917195*x + 4389139

comment: Cremona label 15a1.

15

6481, 521479

1:

1

comment: Cremona label 15a2.

15

6481, 521479

2:

x + 2*y + 1

comment: Cremona label 15a2.

15

6481, 521479

3:

3*x^4 + 5*x^3 - 807*x^2 - 7917*x - 21389

comment: Cremona label 15a2.

15

6481, 521479

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 1340*x^5 - 2690*x^4*y - 27735*x^4 - 52780*x^3*y - 240280*x^3 - 427780*x^2*y - 1030726*x^2 - 1633672*x*y - 2027516*x - 2421360*y - 1210680

comment: Cremona label 15a2.

15

6481, 521479

5:

5*x^12 + 25*x^11 - 8314*x^10 - 264155*x^9 - 2839620*x^8 + 11671680*x^7 + 697318635*x^6 + 9348544029*x^5 + 70589172840*x^4 + 335353371010*x^3 + 1001966981690*x^2 + 1739317411195*x + 1353674938589

comment: Cremona label 15a2.

15

241, -3689

1:

1

comment: Cremona label 15a3.

15

241, -3689

2:

x + 2*y + 1

comment: Cremona label 15a3.

15

241, -3689

3:

3*x^4 + 5*x^3 - 27*x^2 + 27*x - 9

comment: Cremona label 15a3.

15

241, -3689

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 40*x^5 - 90*x^4*y + 45*x^4 + 180*x^3*y - 180*x^2*y - 54*x^2 + 72*x*y + 36*x

comment: Cremona label 15a3.

15

241, -3689

5:

5*x^12 + 25*x^11 - 254*x^10 + 405*x^9 + 1080*x^8 - 6480*x^7 + 13635*x^6 - 15219*x^5 + 11340*x^4 - 8910*x^3 + 7290*x^2 - 3645*x + 729

comment: Cremona label 15a3.

15

-1679, 36631

1:

1

comment: Cremona label 15a4.

15

-1679, 36631

2:

x + 2*y + 1

comment: Cremona label 15a4.

15

-1679, 36631

3:

3*x^4 + 5*x^3 + 213*x^2 - 333*x - 1399

comment: Cremona label 15a4.

15

-1679, 36631

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 360*x^5 + 710*x^4*y - 755*x^4 - 2220*x^3*y - 15100*x^3 - 27980*x^2*y - 13104*x^2 + 1772*x*y - 110764*x - 223300*y - 111650

comment: Cremona label 15a4.

15

-1679, 36631

5:

5*x^12 + 25*x^11 + 2226*x^10 - 6995*x^9 - 171870*x^8 - 865980*x^7 - 15017715*x^6 + 1054911*x^5 - 268389360*x^4 - 202981510*x^3 - 3112930460*x^2 + 5485814805*x + 1362484549

comment: Cremona label 15a4.

15

103681, 33384799

1:

1

comment: Cremona label 15a5.

15

103681, 33384799

2:

x + 2*y + 1

comment: Cremona label 15a5.

15

103681, 33384799

3:

3*x^4 + 5*x^3 - 12957*x^2 - 474477*x - 4861139

comment: Cremona label 15a5.

15

103681, 33384799

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 21590*x^5 - 43190*x^4*y - 1603185*x^4 - 3163180*x^3*y - 50192980*x^3 - 97222780*x^2*y - 756005806*x^2 - 1414788832*x*y - 4726404356*x - 8038019880*y - 4019009940

comment: Cremona label 15a5.

15

103681, 33384799

5:

5*x^12 + 25*x^11 - 133864*x^10 - 15241055*x^9 - 546005370*x^8 + 18305149080*x^7 + 2721020280735*x^6 + 132209507780949*x^5 + 3739290360923490*x^4 + 67158575165185810*x^3 + 759336380220692090*x^2 + 4960315764619126495*x + 14339386207442175479

comment: Cremona label 15a5.

15

5281, 720559

1:

1

comment: Cremona label 15a6.

15

5281, 720559

2:

x + 2*y + 1

comment: Cremona label 15a6.

15

5281, 720559

3:

3*x^4 + 5*x^3 - 657*x^2 - 10557*x - 16389

comment: Cremona label 15a6.

15

5281, 720559

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 1090*x^5 - 2190*x^4*y - 36285*x^4 - 70380*x^3*y - 199080*x^3 - 327780*x^2*y - 1016496*x^2 - 1705212*x*y - 9646776*x - 17588340*y - 8794170

comment: Cremona label 15a6.

15

5281, 720559

5:

5*x^12 + 25*x^11 - 6764*x^10 - 345255*x^9 - 2512620*x^8 + 15744780*x^7 + 288682785*x^6 + 7681524759*x^5 + 143903222190*x^4 + 1066133697210*x^3 - 26348057460*x^2 - 29160614178855*x - 104499307533501

comment: Cremona label 15a6.

15

3841, -238049

1:

1

comment: Cremona label 15a7.

15

3841, -238049

2:

x + 2*y + 1

comment: Cremona label 15a7.

15

3841, -238049

3:

3*x^4 + 5*x^3 - 477*x^2 + 2907*x - 5109

comment: Cremona label 15a7.

15

3841, -238049

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 790*x^5 - 1590*x^4*y + 8895*x^4 + 19380*x^3*y - 41400*x^3 - 102180*x^2*y + 77436*x^2 + 257052*x*y + 1896*x - 253260*y - 126630

comment: Cremona label 15a7.

15

3841, -238049

5:

5*x^12 + 25*x^11 - 4904*x^10 + 84105*x^9 - 318420*x^8 - 6921180*x^7 + 117404685*x^6 - 910793829*x^5 + 4317703290*x^4 - 13215587310*x^3 + 25662477240*x^2 - 28913559795*x + 14453878599

comment: Cremona label 15a7.

15

1, -161

1:

1

comment: Cremona label 15a8.

15

1, -161

2:

x + 2*y + 1

comment: Cremona label 15a8.

15

1, -161

3:

3*x^4 + 5*x^3 + 3*x^2 + 3*x + 1

comment: Cremona label 15a8.

15

1, -161

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 10*x^5 + 10*x^4*y + 15*x^4 + 20*x^3*y + 20*x^3 + 20*x^2*y + 14*x^2 + 8*x*y + 4*x

comment: Cremona label 15a8.

15

1, -161

5:

5*x^12 + 25*x^11 + 56*x^10 + 145*x^9 + 330*x^8 + 480*x^7 + 435*x^6 + 249*x^5 + 90*x^4 + 10*x^3 - 10*x^2 - 5*x - 1

comment: Cremona label 15a8.

17

33, 12015

1:

1

comment: Cremona label 17a1.

17

33, 12015

2:

x + 2*y + 1

comment: Cremona label 17a1.

17

33, 12015

3:

3*x^4 - 3*x^3 - 3*x^2 - 165*x + 41

comment: Cremona label 17a1.

17

33, 12015

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 8*x^5 - 10*x^4*y - 555*x^4 - 1100*x^3*y - 140*x^3 + 820*x^2*y + 232*x^2 - 356*x*y - 3244*x - 6132*y - 3066

comment: Cremona label 17a1.

17

33, 12015

5:

5*x^12 - 15*x^11 - 22*x^10 - 5195*x^9 + 11730*x^8 - 9420*x^7 - 43515*x^6 + 74511*x^5 + 205480*x^4 + 4064730*x^3 - 3156500*x^2 - 380875*x - 9343571

comment: Cremona label 17a1.

17

273, 4455

1:

1

comment: Cremona label 17a2.

17

273, 4455

2:

x + 2*y + 1

comment: Cremona label 17a2.

17

273, 4455

3:

3*x^4 - 3*x^3 - 33*x^2 - 45*x - 19

comment: Cremona label 17a2.

17

273, 4455

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 58*x^5 - 110*x^4*y - 205*x^4 - 300*x^3*y - 340*x^3 - 380*x^2*y - 298*x^2 - 216*x*y - 124*x - 32*y - 16

comment: Cremona label 17a2.

17

273, 4455

5:

5*x^12 - 15*x^11 - 332*x^10 - 1095*x^9 + 30*x^8 + 10080*x^7 + 32835*x^6 + 54201*x^5 + 55630*x^4 + 42330*x^3 + 27950*x^2 + 13875*x + 3259

comment: Cremona label 17a2.

17

4353, 287199

1:

1

comment: Cremona label 17a3.

17

4353, 287199

2:

x + 2*y + 1

comment: Cremona label 17a3.

17

4353, 287199

3:

3*x^4 - 3*x^3 - 543*x^2 - 3717*x - 7261

comment: Cremona label 17a3.

17

4353, 287199

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 908*x^5 - 1810*x^4*y - 13295*x^4 - 24780*x^3*y - 85000*x^3 - 145220*x^2*y - 275086*x^2 - 404952*x*y - 423356*x - 441760*y - 220880

comment: Cremona label 17a3.

17

4353, 287199

5:

5*x^12 - 15*x^11 - 5602*x^10 - 112275*x^9 - 595140*x^8 + 8688240*x^7 + 183220755*x^6 + 1617055917*x^5 + 8586806800*x^4 + 29276716770*x^3 + 63159784210*x^2 + 78941899995*x + 43737794101

comment: Cremona label 17a3.

17

33, -81

1:

1

comment: Cremona label 17a4.

17

33, -81

2:

x + 2*y + 1

comment: Cremona label 17a4.

17

33, -81

3:

3*x^4 - 3*x^3 - 3*x^2 + 3*x - 1

comment: Cremona label 17a4.

17

33, -81

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 8*x^5 - 10*x^4*y + 5*x^4 + 20*x^3*y - 20*x^2*y - 6*x^2 + 8*x*y + 4*x

comment: Cremona label 17a4.

17

33, -81

5:

5*x^12 - 15*x^11 - 22*x^10 + 125*x^9 - 240*x^8 + 240*x^7 - 45*x^6 - 123*x^5 + 100*x^4 - 30*x^3 + 10*x^2 - 5*x + 1

comment: Cremona label 17a4.

19

448, 10088

1:

1

comment: Cremona label 19a1.

19

448, 10088

2:

2*y + 1

comment: Cremona label 19a1.

19

448, 10088

3:

3*x^4 + 4*x^3 - 54*x^2 - 177*x - 140

comment: Cremona label 19a1.

19

448, 10088

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 180*x^4*y - 90*x^4 - 1180*x^3*y - 590*x^3 - 2800*x^2*y - 1400*x^2 - 3244*x*y - 1622*x - 1922*y - 961

comment: Cremona label 19a1.

19

448, 10088

5:

5*x^12 + 20*x^11 - 542*x^10 - 6325*x^9 - 25320*x^8 - 18540*x^7 + 228465*x^6 + 1164844*x^5 + 3049800*x^4 + 4731595*x^3 + 3777860*x^2 + 679090*x - 601241

comment: Cremona label 19a1.

19

36928, 7096328

1:

1

comment: Cremona label 19a2.

19

36928, 7096328

2:

2*y + 1

comment: Cremona label 19a2.

19

36928, 7096328

3:

3*x^4 + 4*x^3 - 4614*x^2 - 101637*x - 625240

comment: Cremona label 19a2.

19

36928, 7096328

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 15380*x^4*y - 7690*x^4 - 677580*x^3*y - 338790*x^3 - 12504800*x^2*y - 6252400*x^2 - 109213724*x*y - 54606862*x - 372335042*y - 186167521

comment: Cremona label 19a2.

19

36928, 7096328

5:

5*x^12 + 20*x^11 - 47662*x^10 - 3280025*x^9 - 71748420*x^8 + 1338090660*x^7 + 123749656665*x^6 + 3627671770564*x^5 + 61697376941000*x^4 + 665631175640095*x^3 + 4518723451195760*x^2 + 17718617108107290*x + 30741389421937039

comment: Cremona label 19a2.

19

-32, 8

1:

1

comment: Cremona label 19a3.

19

-32, 8

2:

2*y + 1

comment: Cremona label 19a3.

19

-32, 8

3:

3*x^4 + 4*x^3 + 6*x^2 + 3*x

comment: Cremona label 19a3.

19

-32, 8

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 + 20*x^4*y + 10*x^4 + 20*x^3*y + 10*x^3 - 4*x*y - 2*x - 2*y - 1

comment: Cremona label 19a3.

19

-32, 8

5:

5*x^12 + 20*x^11 + 78*x^10 + 175*x^9 + 180*x^8 + 60*x^7 - 135*x^6 - 236*x^5 - 200*x^4 - 105*x^3 - 40*x^2 - 10*x - 1

comment: Cremona label 19a3.

20

-176, -2368

1:

1

comment: Cremona label 20a1.

20

-176, -2368

2:

2*y

comment: Cremona label 20a1.

20

-176, -2368

3:

3*x^4 + 4*x^3 + 24*x^2 + 48*x

comment: Cremona label 20a1.

20

-176, -2368

4:

4*x^6*y + 8*x^5*y + 80*x^4*y + 320*x^3*y - 256*x*y - 512*y

comment: Cremona label 20a1.

20

-176, -2368

5:

5*x^12 + 20*x^11 + 264*x^10 + 1840*x^9 + 2880*x^8 + 3840*x^7 - 11520*x^6 - 54272*x^5 - 143360*x^4 - 184320*x^3 - 163840*x^2 - 163840*x - 65536

comment: Cremona label 20a1.

20

64, -352

1:

1

comment: Cremona label 20a2.

20

64, -352

2:

2*y

comment: Cremona label 20a2.

20

64, -352

3:

3*x^4 + 4*x^3 - 6*x^2 - 1

comment: Cremona label 20a2.

20

64, -352

4:

4*x^6*y + 8*x^5*y - 20*x^4*y - 20*x^2*y - 8*x*y + 4*y

comment: Cremona label 20a2.

20

64, -352

5:

5*x^12 + 20*x^11 - 46*x^10 - 80*x^9 - 105*x^8 - 360*x^7 + 60*x^6 + 304*x^5 + 35*x^4 - 140*x^3 + 50*x^2 + 1

comment: Cremona label 20a2.

20

1744, 110528

1:

1

comment: Cremona label 20a3.

20

1744, 110528

2:

2*y

comment: Cremona label 20a3.

20

1744, 110528

3:

3*x^4 + 4*x^3 - 216*x^2 - 1680*x - 1856

comment: Cremona label 20a3.

20

1744, 110528

4:

4*x^6*y + 8*x^5*y - 720*x^4*y - 11200*x^3*y - 37120*x^2*y - 95488*x*y - 359936*y

comment: Cremona label 20a3.

20

1744, 110528

5:

5*x^12 + 20*x^11 - 2216*x^10 - 56080*x^9 - 295680*x^8 + 541440*x^7 + 12476160*x^6 + 140698624*x^5 + 1138421760*x^4 + 4229263360*x^3 + 1501184000*x^2 - 26636288000*x - 50044534784

comment: Cremona label 20a3.

20

1984, 88352

1:

1

comment: Cremona label 20a4.

20

1984, 88352

2:

2*y

comment: Cremona label 20a4.

20

1984, 88352

3:

3*x^4 + 4*x^3 - 246*x^2 - 1392*x - 2145

comment: Cremona label 20a4.

20

1984, 88352

4:

4*x^6*y + 8*x^5*y - 820*x^4*y - 9280*x^3*y - 42900*x^2*y - 93256*x*y - 78812*y

comment: Cremona label 20a4.

20

1984, 88352

5:

5*x^12 + 20*x^11 - 2526*x^10 - 47360*x^9 - 308745*x^8 + 369240*x^7 + 20356380*x^6 + 160876048*x^5 + 699937315*x^4 + 1902576180*x^3 + 3236327810*x^2 + 3177780560*x + 1385244449

comment: Cremona label 20a4.

21

193, 575

1:

1

comment: Cremona label 21a1.

21

193, 575

2:

x + 2*y

comment: Cremona label 21a1.

21

193, 575

3:

3*x^4 + x^3 - 24*x^2 - 12*x - 17

comment: Cremona label 21a1.

21

193, 575

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 40*x^5 - 80*x^4*y - 40*x^4 - 80*x^3*y - 170*x^3 - 340*x^2*y - 49*x^2 - 98*x*y + 120*x + 240*y

comment: Cremona label 21a1.

21

193, 575

5:

5*x^12 + 5*x^11 - 247*x^10 - 460*x^9 - 1965*x^8 - 570*x^7 + 19425*x^6 + 17223*x^5 - 24105*x^4 - 11995*x^3 + 48920*x^2 + 24980*x + 6833

comment: Cremona label 21a1.

21

2353, 113975

1:

1

comment: Cremona label 21a2.

21

2353, 113975

2:

x + 2*y

comment: Cremona label 21a2.

21

2353, 113975

3:

3*x^4 + x^3 - 294*x^2 - 1632*x - 2537

comment: Cremona label 21a2.

21

2353, 113975

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 490*x^5 - 980*x^4*y - 5440*x^4 - 10880*x^3*y - 25370*x^3 - 50740*x^2*y - 55849*x^2 - 111698*x*y - 47310*x - 94620*y

comment: Cremona label 21a2.

21

2353, 113975

5:

5*x^12 + 5*x^11 - 3037*x^10 - 52660*x^9 - 290865*x^8 + 1371030*x^7 + 32017125*x^6 + 236430483*x^5 + 1011228045*x^4 + 2750749805*x^3 + 4764625970*x^2 + 4895970080*x + 2328335993

comment: Cremona label 21a2.

21

1873, -80569

1:

1

comment: Cremona label 21a3.

21

1873, -80569

2:

x + 2*y

comment: Cremona label 21a3.

21

1873, -80569

3:

3*x^4 + x^3 - 234*x^2 + 1080*x - 1431

comment: Cremona label 21a3.

21

1873, -80569

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 390*x^5 - 780*x^4*y + 3600*x^4 + 7200*x^3*y - 14310*x^3 - 28620*x^2*y + 26649*x^2 + 53298*x*y - 17982*x - 35964*y

comment: Cremona label 21a3.

21

1873, -80569

5:

5*x^12 + 5*x^11 - 2417*x^10 + 33420*x^9 - 134055*x^8 - 971190*x^7 + 15198435*x^6 - 91086363*x^5 + 322134165*x^4 - 740310435*x^3 + 1146534750*x^2 - 1161297000*x + 599878791

comment: Cremona label 21a3.

21

-47, 71

1:

1

comment: Cremona label 21a4.

21

-47, 71

2:

x + 2*y

comment: Cremona label 21a4.

21

-47, 71

3:

3*x^4 + x^3 + 6*x^2 - 1

comment: Cremona label 21a4.

21

-47, 71

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y + 10*x^5 + 20*x^4*y - 10*x^3 - 20*x^2*y - x^2 - 2*x*y - 2*x - 4*y

comment: Cremona label 21a4.

21

-47, 71

5:

5*x^12 + 5*x^11 + 63*x^10 + 20*x^9 - 105*x^8 - 90*x^7 - 315*x^6 - 93*x^5 - 135*x^4 - 35*x^3 - 50*x^2 + 1

comment: Cremona label 21a4.

21

37633, 7300511

1:

1

comment: Cremona label 21a5.

21

37633, 7300511

2:

x + 2*y

comment: Cremona label 21a5.

21

37633, 7300511

3:

3*x^4 + x^3 - 4704*x^2 - 102180*x - 623171

comment: Cremona label 21a5.

21

37633, 7300511

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 7840*x^5 - 15680*x^4*y - 340600*x^4 - 681200*x^3*y - 6231710*x^3 - 12463420*x^2*y - 54029251*x^2 - 108058502*x*y - 182951472*x - 365902944*y

comment: Cremona label 21a5.

21

37633, 7300511

5:

5*x^12 + 5*x^11 - 48607*x^10 - 3251380*x^9 - 66965655*x^8 + 1546097010*x^7 + 128358126435*x^6 + 3678915326277*x^5 + 61764374659815*x^4 + 659810372160365*x^3 + 4441366548376400*x^2 + 17281054070793500*x + 29764529570370011

comment: Cremona label 21a5.

21

1633, 185039

1:

1

comment: Cremona label 21a6.

21

1633, 185039

2:

x + 2*y

comment: Cremona label 21a6.

21

1633, 185039

3:

3*x^4 + x^3 - 204*x^2 - 2604*x - 1373

comment: Cremona label 21a6.

21

1633, 185039

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 340*x^5 - 680*x^4*y - 8680*x^4 - 17360*x^3*y - 13730*x^3 - 27460*x^2*y - 60397*x^2 - 120794*x*y - 660060*x - 1320120*y

comment: Cremona label 21a6.

21

1633, 185039

5:

5*x^12 + 5*x^11 - 2107*x^10 - 83140*x^9 - 183225*x^8 + 1647150*x^7 + 1797285*x^6 + 173176659*x^5 + 2900575515*x^4 + 15997167725*x^3 - 6582727180*x^2 - 186615447340*x - 494716763323

comment: Cremona label 21a6.

24

208, -2240

1:

1

comment: Cremona label 24a1.

24

208, -2240

2:

2*y

comment: Cremona label 24a1.

24

208, -2240

3:

3*x^4 - 4*x^3 - 24*x^2 + 48*x - 32

comment: Cremona label 24a1.

24

208, -2240

4:

4*x^6*y - 8*x^5*y - 80*x^4*y + 320*x^3*y - 640*x^2*y + 512*x*y

comment: Cremona label 24a1.

24

208, -2240

5:

5*x^12 - 20*x^11 - 232*x^10 + 1840*x^9 - 6240*x^8 + 7680*x^7 + 19200*x^6 - 79872*x^5 + 107520*x^4 - 81920*x^3 + 81920*x^2 - 81920*x + 32768

comment: Cremona label 24a1.

24

1168, 38080

1:

1

comment: Cremona label 24a2.

24

1168, 38080

2:

2*y

comment: Cremona label 24a2.

24

1168, 38080

3:

3*x^4 - 4*x^3 - 144*x^2 - 432*x - 432

comment: Cremona label 24a2.

24

1168, 38080

4:

4*x^6*y - 8*x^5*y - 480*x^4*y - 2880*x^3*y - 8640*x^2*y - 10368*x*y

comment: Cremona label 24a2.

24

1168, 38080

5:

5*x^12 - 20*x^11 - 1472*x^10 - 11760*x^9 - 19440*x^8 + 362880*x^7 + 3110400*x^6 + 11155968*x^5 + 22705920*x^4 + 41057280*x^3 + 89579520*x^2 + 134369280*x + 80621568

comment: Cremona label 24a2.

24

3088, -171584

1:

1

comment: Cremona label 24a3.

24

3088, -171584

2:

2*y

comment: Cremona label 24a3.

24

3088, -171584

3:

3*x^4 - 4*x^3 - 384*x^2 + 2640*x - 4976

comment: Cremona label 24a3.

24

3088, -171584

4:

4*x^6*y - 8*x^5*y - 1280*x^4*y + 17600*x^3*y - 99520*x^2*y + 265088*x*y - 274944*y

comment: Cremona label 24a3.

24

3088, -171584

5:

5*x^12 - 20*x^11 - 3952*x^10 + 88720*x^9 - 680880*x^8 - 1587840*x^7 + 75970560*x^6 - 719021568*x^5 + 3804675840*x^4 - 12630901760*x^3 + 26271641600*x^2 - 31522304000*x + 16750309376

comment: Cremona label 24a3.

24

-32, -224

1:

1

comment: Cremona label 24a4.

24

-32, -224

2:

2*y

comment: Cremona label 24a4.

24

-32, -224

3:

3*x^4 - 4*x^3 + 6*x^2 - 1

comment: Cremona label 24a4.

24

-32, -224

4:

4*x^6*y - 8*x^5*y + 20*x^4*y - 20*x^2*y + 8*x*y - 4*y

comment: Cremona label 24a4.

24

-32, -224

5:

5*x^12 - 20*x^11 + 78*x^10 - 80*x^9 - 105*x^8 + 360*x^7 - 540*x^6 + 432*x^5 - 285*x^4 + 140*x^3 - 50*x^2 + 1

comment: Cremona label 24a4.

24

18448, 2505664

1:

1

comment: Cremona label 24a5.

24

18448, 2505664

2:

2*y

comment: Cremona label 24a5.

24

18448, 2505664

3:

3*x^4 - 4*x^3 - 2304*x^2 - 33264*x - 136368

comment: Cremona label 24a5.

24

18448, 2505664

4:

4*x^6*y - 8*x^5*y - 7680*x^4*y - 221760*x^3*y - 2727360*x^2*y - 15940224*x*y - 36426240*y

comment: Cremona label 24a5.

24

18448, 2505664

5:

5*x^12 - 20*x^11 - 23792*x^10 - 1022640*x^9 - 12322800*x^8 + 304560000*x^7 + 14343644160*x^6 + 268778985984*x^5 + 3006611101440*x^4 + 21536042572800*x^3 + 97485873131520*x^2 + 255498303836160*x + 296741724106752

comment: Cremona label 24a5.

24

-752, 150976

1:

1

comment: Cremona label 24a6.

24

-752, 150976

2:

2*y

comment: Cremona label 24a6.

24

-752, 150976

3:

3*x^4 - 4*x^3 + 96*x^2 - 2160*x + 464

comment: Cremona label 24a6.

24

-752, 150976

4:

4*x^6*y - 8*x^5*y + 320*x^4*y - 14400*x^3*y + 9280*x^2*y + 42368*x*y - 1007104*y

comment: Cremona label 24a6.

24

-752, 150976

5:

5*x^12 - 20*x^11 + 1008*x^10 - 69680*x^9 + 178320*x^8 - 858240*x^7 - 6819840*x^6 + 45230592*x^5 - 989026560*x^4 + 9864535040*x^3 - 11066470400*x^2 + 58784256000*x - 261141254144

comment: Cremona label 24a6.

26

217, 6371

1:

1

comment: Cremona label 26a1.

26

217, 6371

2:

x + 2*y + 1

comment: Cremona label 26a1.

26

217, 6371

3:

3*x^4 + x^3 - 27*x^2 - 93*x - 28

comment: Cremona label 26a1.

26

217, 6371

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 44*x^5 - 90*x^4*y - 355*x^4 - 620*x^3*y - 590*x^3 - 560*x^2*y - 587*x^2 - 614*x*y - 1016*x - 1418*y - 709

comment: Cremona label 26a1.

26

217, 6371

5:

5*x^12 + 5*x^11 - 278*x^10 - 3035*x^9 - 4335*x^8 + 5850*x^7 + 18780*x^6 + 113306*x^5 + 465135*x^4 + 734385*x^3 - 7430*x^2 - 867535*x - 659397

comment: Cremona label 26a1.

26

22057, 3275819

1:

1

comment: Cremona label 26a2.

26

22057, 3275819

2:

x + 2*y + 1

comment: Cremona label 26a2.

26

22057, 3275819

3:

3*x^4 + x^3 - 2757*x^2 - 45957*x - 214970

comment: Cremona label 26a2.

26

22057, 3275819

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 4594*x^5 - 9190*x^4*y - 157785*x^4 - 306380*x^3*y - 2302890*x^3 - 4299400*x^2*y - 16442831*x^2 - 28586262*x*y - 51407462*x - 74228662*y - 37114331

comment: Cremona label 26a2.

26

22057, 3275819

5:

5*x^12 + 5*x^11 - 28488*x^10 - 1464495*x^9 - 23261205*x^8 + 402997530*x^7 + 25899141120*x^6 + 570108913658*x^5 + 7344224616035*x^4 + 60181736173665*x^3 + 310697735610840*x^2 + 927108232309045*x + 1224529916366109

comment: Cremona label 26a2.

26

-23, -181

1:

1

comment: Cremona label 26a3.

26

-23, -181

2:

x + 2*y + 1

comment: Cremona label 26a3.

26

-23, -181

3:

3*x^4 + x^3 + 3*x^2 + 3*x

comment: Cremona label 26a3.

26

-23, -181

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 6*x^5 + 10*x^4*y + 15*x^4 + 20*x^3*y + 10*x^3 - x^2 - 2*x*y - 2*x - 2*y - 1

comment: Cremona label 26a3.

26

-23, -181

5:

5*x^12 + 5*x^11 + 32*x^10 + 105*x^9 + 45*x^8 + 30*x^7 - 30*x^6 - 52*x^5 - 65*x^4 - 35*x^3 - 10*x^2 - 5*x - 1

comment: Cremona label 26a3.

26

129, -2241

1:

1

comment: Cremona label 26b1.

26

129, -2241

2:

x + 2*y + 1

comment: Cremona label 26b1.

26

129, -2241

3:

3*x^4 - 3*x^3 - 15*x^2 + 39*x - 16

comment: Cremona label 26b1.

26

129, -2241

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 28*x^5 - 50*x^4*y + 105*x^4 + 260*x^3*y - 30*x^3 - 320*x^2*y - 47*x^2 + 226*x*y + 24*x - 178*y - 89

comment: Cremona label 26b1.

26

129, -2241

5:

5*x^12 - 15*x^11 - 146*x^10 + 1385*x^9 - 3435*x^8 + 2370*x^7 + 4380*x^6 - 20358*x^5 + 49015*x^4 - 61715*x^3 + 26150*x^2 + 12285*x - 10945

comment: Cremona label 26b1.

26

10209, 1131759

1:

1

comment: Cremona label 26b2.

26

10209, 1131759

2:

x + 2*y + 1

comment: Cremona label 26b2.

26

10209, 1131759

3:

3*x^4 - 3*x^3 - 1275*x^2 - 15081*x - 41386

comment: Cremona label 26b2.

26

10209, 1131759

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 2128*x^5 - 4250*x^4*y - 52395*x^4 - 100540*x^3*y - 464130*x^3 - 827720*x^2*y - 2426177*x^2 - 4024634*x*y - 9693996*x - 15363358*y - 7681679

comment: Cremona label 26b2.

26

10209, 1131759

5:

5*x^12 - 15*x^11 - 13166*x^10 - 464815*x^9 - 3666885*x^8 + 75268470*x^7 + 2349850830*x^6 + 37621273212*x^5 + 395629964815*x^4 + 2168063901385*x^3 + 1352220716600*x^2 - 39007322673165*x - 123235646253535

comment: Cremona label 26b2.

27

0, 5832

1:

1

comment: Cremona label 27a1.

27

0, 5832

2:

2*y + 1

comment: Cremona label 27a1.

27

0, 5832

3:

3*x^4 - 81*x

comment: Cremona label 27a1.

27

0, 5832

4:

4*x^6*y + 2*x^6 - 540*x^3*y - 270*x^3 - 1458*y - 729

comment: Cremona label 27a1.

27

0, 5832

5:

5*x^12 - 2565*x^9 - 10935*x^6 + 492075*x^3 - 531441

comment: Cremona label 27a1.

27

12960, 1475496

1:

1

comment: Cremona label 27a2.

27

12960, 1475496

2:

2*y + 1

comment: Cremona label 27a2.

27

12960, 1475496

3:

3*x^4 - 1620*x^2 - 20493*x - 72900

comment: Cremona label 27a2.

27

12960, 1475496

4:

4*x^6*y + 2*x^6 - 5400*x^4*y - 2700*x^4 - 136620*x^3*y - 68310*x^3 - 1458000*x^2*y - 729000*x^2 - 7377480*x*y - 3688740*x - 14593122*y - 7296561

comment: Cremona label 27a2.

27

12960, 1475496

5:

5*x^12 - 16740*x^10 - 648945*x^9 - 7654500*x^8 + 110662200*x^7 + 5204961585*x^6 + 86648502600*x^5 + 847565726400*x^4 + 5279707394775*x^3 + 20719024546500*x^2 + 46938091434300*x + 46944266247279

comment: Cremona label 27a2.

27

0, -216

1:

1

comment: Cremona label 27a3.

27

0, -216

2:

2*y + 1

comment: Cremona label 27a3.

27

0, -216

3:

3*x^4 + 3*x

comment: Cremona label 27a3.

27

0, -216

4:

4*x^6*y + 2*x^6 + 20*x^3*y + 10*x^3 - 2*y - 1

comment: Cremona label 27a3.

27

0, -216

5:

5*x^12 + 95*x^9 - 15*x^6 - 25*x^3 - 1

comment: Cremona label 27a3.

27

1440, -54648

1:

1

comment: Cremona label 27a4.

27

1440, -54648

2:

2*y + 1

comment: Cremona label 27a4.

27

1440, -54648

3:

3*x^4 - 180*x^2 + 759*x - 900

comment: Cremona label 27a4.

27

1440, -54648

4:

4*x^6*y + 2*x^6 - 600*x^4*y - 300*x^4 + 5060*x^3*y + 2530*x^3 - 18000*x^2*y - 9000*x^2 + 30360*x*y + 15180*x - 20018*y - 10009

comment: Cremona label 27a4.

27

1440, -54648

5:

5*x^12 - 1860*x^10 + 24035*x^9 - 94500*x^8 - 455400*x^7 + 7139865*x^6 - 39619800*x^5 + 129182400*x^4 - 268236925*x^3 + 350878500*x^2 - 264966900*x + 88333919

comment: Cremona label 27a4.

30

-71, -1837

1:

1

comment: Cremona label 30a1.

30

-71, -1837

2:

x + 2*y + 1

comment: Cremona label 30a1.

30

-71, -1837

3:

3*x^4 + x^3 + 9*x^2 + 27*x

comment: Cremona label 30a1.

30

-71, -1837

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 16*x^5 + 30*x^4*y + 105*x^4 + 180*x^3*y + 90*x^3 - 27*x^2 - 54*x*y - 108*x - 162*y - 81

comment: Cremona label 30a1.

30

-71, -1837

5:

5*x^12 + 5*x^11 + 94*x^10 + 885*x^9 + 405*x^8 + 810*x^7 - 1620*x^6 - 4158*x^5 - 14985*x^4 - 20655*x^3 - 7290*x^2 - 10935*x - 6561

comment: Cremona label 30a1.

30

889, -24013

1:

1

comment: Cremona label 30a2.

30

889, -24013

2:

x + 2*y + 1

comment: Cremona label 30a2.

30

889, -24013

3:

3*x^4 + x^3 - 111*x^2 + 315*x - 316

comment: Cremona label 30a2.

30

889, -24013

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 184*x^5 - 370*x^4*y + 865*x^4 + 2100*x^3*y - 2110*x^3 - 6320*x^2*y + 409*x^2 + 7138*x*y + 4236*x + 1334*y + 667

comment: Cremona label 30a2.

30

889, -24013

5:

5*x^12 + 5*x^11 - 1146*x^10 + 9605*x^9 - 28455*x^8 - 144990*x^7 + 1641960*x^6 - 5794194*x^5 + 10171935*x^4 - 16411535*x^3 + 40808650*x^2 - 65380875*x + 38908171

comment: Cremona label 30a2.

30

649, 54107

1:

1

comment: Cremona label 30a3.

30

649, 54107

2:

x + 2*y + 1

comment: Cremona label 30a3.

30

649, 54107

3:

3*x^4 + x^3 - 81*x^2 - 765*x - 246

comment: Cremona label 30a3.

30

649, 54107

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 134*x^5 - 270*x^4*y - 2685*x^4 - 5100*x^3*y - 5010*x^3 - 4920*x^2*y - 9591*x^2 - 14262*x*y - 65514*x - 116766*y - 58383

comment: Cremona label 30a3.

30

649, 54107

5:

5*x^12 + 5*x^11 - 836*x^10 - 24495*x^9 - 37305*x^8 + 184410*x^7 - 86040*x^6 + 7897146*x^5 + 100934235*x^4 + 413663265*x^3 - 50217300*x^2 - 1932676875*x - 3781467639

comment: Cremona label 30a3.

30

3289, 162467

1:

1

comment: Cremona label 30a4.

30

3289, 162467

2:

x + 2*y + 1

comment: Cremona label 30a4.

30

3289, 162467

3:

3*x^4 + x^3 - 411*x^2 - 2325*x - 4886

comment: Cremona label 30a4.

30

3289, 162467

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 684*x^5 - 1370*x^4*y - 8435*x^4 - 15500*x^3*y - 56610*x^3 - 97720*x^2*y - 159921*x^2 - 222122*x*y - 42304*x + 137514*y + 68757

comment: Cremona label 30a4.

30

3289, 162467

5:

5*x^12 + 5*x^11 - 4246*x^10 - 74995*x^9 - 547905*x^8 + 2745510*x^7 + 89732010*x^6 + 658925736*x^5 + 2161622535*x^4 + 6474566765*x^3 + 37212338300*x^2 + 129009231875*x + 157940631581

comment: Cremona label 30a4.

30

13849, -1629757

1:

1

comment: Cremona label 30a5.

30

13849, -1629757

2:

x + 2*y + 1

comment: Cremona label 30a5.

30

13849, -1629757

3:

3*x^4 + x^3 - 1731*x^2 + 22347*x - 81370

comment: Cremona label 30a5.

30

13849, -1629757

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 2884*x^5 - 5770*x^4*y + 71605*x^4 + 148980*x^3*y - 739210*x^3 - 1627400*x^2*y + 3403003*x^2 + 8433406*x*y - 4320408*x - 17074222*y - 8537111

comment: Cremona label 30a5.

30

13849, -1629757

5:

5*x^12 + 5*x^11 - 17886*x^10 + 701885*x^9 - 8208645*x^8 - 136265490*x^7 + 6273510030*x^6 - 106131701028*x^5 + 1059966566415*x^4 - 6753471981155*x^3 + 27147713483560*x^2 - 63136377704985*x + 65053218492289

comment: Cremona label 30a5.

30

16009, 2021723

1:

1

comment: Cremona label 30a6.

30

16009, 2021723

2:

x + 2*y + 1

comment: Cremona label 30a6.

30

16009, 2021723

3:

3*x^4 + x^3 - 2001*x^2 - 28413*x - 113590

comment: Cremona label 30a6.

30

16009, 2021723

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 3334*x^5 - 6670*x^4*y - 98045*x^4 - 189420*x^3*y - 1230610*x^3 - 2271800*x^2*y - 7566647*x^2 - 12861494*x*y - 20366058*x - 27870622*y - 13935311

comment: Cremona label 30a6.

30

16009, 2021723

5:

5*x^12 + 5*x^11 - 20676*x^10 - 906415*x^9 - 12353145*x^8 + 179291610*x^7 + 9922720680*x^6 + 186095140602*x^5 + 2036051546715*x^4 + 14220483181345*x^3 + 63637063284460*x^2 + 170849057821365*x + 215621160293449

comment: Cremona label 30a6.

30

256009, 129533723

1:

1

comment: Cremona label 30a7.

30

256009, 129533723

2:

x + 2*y + 1

comment: Cremona label 30a7.

30

256009, 129533723

3:

3*x^4 + x^3 - 32001*x^2 - 1804413*x - 28596590

comment: Cremona label 30a7.

30

256009, 129533723

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 53334*x^5 - 106670*x^4*y - 6068045*x^4 - 12029420*x^3*y - 291980610*x^3 - 571931800*x^2*y - 6730453647*x^2 - 12888975494*x*y - 63172026058*x - 113455076622*y - 56727538311

comment: Cremona label 30a7.

30

256009, 129533723

5:

5*x^12 + 5*x^11 - 330676*x^10 - 57246415*x^9 - 3029708145*x^8 + 189903041610*x^7 + 40232796055680*x^6 + 2988378659527602*x^5 + 130263445691426715*x^4 + 3615228314716481345*x^3 + 63238975613649589460*x^2 + 639520983122746596365*x + 2863117274891524566449

comment: Cremona label 30a7.

30

21769, 437147

1:

1

comment: Cremona label 30a8.

30

21769, 437147

2:

x + 2*y + 1

comment: Cremona label 30a8.

30

21769, 437147

3:

3*x^4 + x^3 - 2721*x^2 - 6525*x - 206206

comment: Cremona label 30a8.

30

21769, 437147

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 4534*x^5 - 9070*x^4*y - 26285*x^4 - 43500*x^3*y - 2083810*x^3 - 4124120*x^2*y - 4240991*x^2 - 4357862*x*y + 180119286*x + 364596434*y + 182298217

comment: Cremona label 30a8.

30

21769, 437147

5:

5*x^12 + 5*x^11 - 28116*x^10 - 215695*x^9 - 21749505*x^8 + 40623210*x^7 + 27950682960*x^6 + 86398546626*x^5 - 5032094808165*x^4 - 5251489835135*x^3 + 945564499735300*x^2 + 2260536195148125*x + 9630452184985441

comment: Cremona label 30a8.

32

-192, 0

1:

1

comment: Cremona label 32a1.

32

-192, 0

2:

2*y

comment: Cremona label 32a1.

32

-192, 0

3:

3*x^4 + 24*x^2 - 16

comment: Cremona label 32a1.

32

-192, 0

4:

4*x^6*y + 80*x^4*y - 320*x^2*y - 256*y

comment: Cremona label 32a1.

32

-192, 0

5:

5*x^12 + 248*x^10 - 1680*x^8 - 19200*x^6 - 32000*x^4 - 51200*x^2 + 4096

comment: Cremona label 32a1.

32

48, 0

1:

1

comment: Cremona label 32a2.

32

48, 0

2:

2*y

comment: Cremona label 32a2.

32

48, 0

3:

3*x^4 - 6*x^2 - 1

comment: Cremona label 32a2.

32

48, 0

4:

4*x^6*y - 20*x^4*y - 20*x^2*y + 4*y

comment: Cremona label 32a2.

32

48, 0

5:

5*x^12 - 62*x^10 - 105*x^8 + 300*x^6 - 125*x^4 + 50*x^2 + 1

comment: Cremona label 32a2.

32

528, 12096

1:

1

comment: Cremona label 32a3.

32

528, 12096

2:

2*y

comment: Cremona label 32a3.

32

528, 12096

3:

3*x^4 - 66*x^2 - 168*x - 121

comment: Cremona label 32a3.

32

528, 12096

4:

4*x^6*y - 220*x^4*y - 1120*x^3*y - 2420*x^2*y - 2464*x*y - 948*y

comment: Cremona label 32a3.

32

528, 12096

5:

5*x^12 - 682*x^10 - 5320*x^9 - 12705*x^8 + 36960*x^7 + 352260*x^6 + 1179024*x^5 + 2309395*x^4 + 2899680*x^3 + 2360710*x^2 + 1179640*x + 285097

comment: Cremona label 32a3.

32

528, -12096

1:

1

comment: Cremona label 32a4.

32

528, -12096

2:

2*y

comment: Cremona label 32a4.

32

528, -12096

3:

3*x^4 - 66*x^2 + 168*x - 121

comment: Cremona label 32a4.

32

528, -12096

4:

4*x^6*y - 220*x^4*y + 1120*x^3*y - 2420*x^2*y + 2464*x*y - 948*y

comment: Cremona label 32a4.

32

528, -12096

5:

5*x^12 - 682*x^10 + 5320*x^9 - 12705*x^8 - 36960*x^7 + 352260*x^6 - 1179024*x^5 + 2309395*x^4 - 2899680*x^3 + 2360710*x^2 - 1179640*x + 285097

comment: Cremona label 32a4.

33

553, -4085

1:

1

comment: Cremona label 33a1.

33

553, -4085

2:

x + 2*y

comment: Cremona label 33a1.

33

553, -4085

3:

3*x^4 + 5*x^3 - 66*x^2 - 121

comment: Cremona label 33a1.

33

553, -4085

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 110*x^5 - 220*x^4*y - 1210*x^3 - 2420*x^2*y - 605*x^2 - 1210*x*y + 2662*x + 5324*y

comment: Cremona label 33a1.

33

553, -4085

5:

5*x^12 + 25*x^11 - 657*x^10 - 1100*x^9 - 12705*x^8 - 54450*x^7 + 353925*x^6 + 597135*x^5 - 1497375*x^4 - 2562175*x^3 + 8052550*x^2 + 1771561

comment: Cremona label 33a1.

33

313, 5491

1:

1

comment: Cremona label 33a2.

33

313, 5491

2:

x + 2*y

comment: Cremona label 33a2.

33

313, 5491

3:

3*x^4 + 5*x^3 - 36*x^2 - 108*x - 81

comment: Cremona label 33a2.

33

313, 5491

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 60*x^5 - 120*x^4*y - 360*x^4 - 720*x^3*y - 810*x^3 - 1620*x^2*y - 837*x^2 - 1674*x*y - 324*x - 648*y

comment: Cremona label 33a2.

33

313, 5491

5:

5*x^12 + 25*x^11 - 347*x^10 - 4020*x^9 - 16605*x^8 - 23490*x^7 + 63585*x^6 + 379539*x^5 + 874395*x^4 + 1174905*x^3 + 976860*x^2 + 481140*x + 111537

comment: Cremona label 33a2.

33

7033, -589229

1:

1

comment: Cremona label 33a3.

33

7033, -589229

2:

x + 2*y

comment: Cremona label 33a3.

33

7033, -589229

3:

3*x^4 + 5*x^3 - 876*x^2 + 7452*x - 18211

comment: Cremona label 33a3.

33

7033, -589229

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 1460*x^5 - 2920*x^4*y + 24840*x^4 + 49680*x^3*y - 182110*x^3 - 364220*x^2*y + 634273*x^2 + 1268546*x*y - 852644*x - 1705288*y

comment: Cremona label 33a3.

33

7033, -589229

5:

5*x^12 + 25*x^11 - 9027*x^10 + 221380*x^9 - 1353255*x^8 - 29954790*x^7 + 752658435*x^6 - 8205593271*x^5 + 54101305395*x^4 - 230343800095*x^3 + 629579438260*x^2 - 1026742434660*x + 778473771067

comment: Cremona label 33a3.

33

-2087, -31805

1:

1

comment: Cremona label 33a4.

33

-2087, -31805

2:

x + 2*y

comment: Cremona label 33a4.

33

-2087, -31805

3:

3*x^4 + 5*x^3 + 264*x^2 + 660*x - 1661

comment: Cremona label 33a4.

33

-2087, -31805

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y + 440*x^5 + 880*x^4*y + 2200*x^4 + 4400*x^3*y - 16610*x^3 - 33220*x^2*y - 27665*x^2 - 55330*x*y - 194568*x - 389136*y

comment: Cremona label 33a4.

33

-2087, -31805

5:

5*x^12 + 25*x^11 + 2753*x^10 + 25300*x^9 - 124905*x^8 - 166650*x^7 - 24726075*x^6 - 110235345*x^5 - 725228625*x^4 - 1374895775*x^3 - 9415760200*x^2 - 21868995500*x - 4834523419

comment: Cremona label 33a4.

34

145, -1081

1:

1

comment: Cremona label 34a1.

34

145, -1081

2:

x + 2*y

comment: Cremona label 34a1.

34

145, -1081

3:

3*x^4 + x^3 - 18*x^2 + 12*x - 8

comment: Cremona label 34a1.

34

145, -1081

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 30*x^5 - 60*x^4*y + 40*x^4 + 80*x^3*y - 80*x^3 - 160*x^2*y + 16*x^2 + 32*x*y + 32*x + 64*y

comment: Cremona label 34a1.

34

145, -1081

5:

5*x^12 + 5*x^11 - 185*x^10 + 320*x^9 - 660*x^8 - 1440*x^7 + 7200*x^6 - 4160*x^5 - 3840*x^4 - 1280*x^3 + 8960*x^2 - 5120*x + 1024

comment: Cremona label 34a1.

34

2065, -93817

1:

1

comment: Cremona label 34a2.

34

2065, -93817

2:

x + 2*y

comment: Cremona label 34a2.

34

2065, -93817

3:

3*x^4 + x^3 - 258*x^2 + 1260*x - 1744

comment: Cremona label 34a2.

34

2065, -93817

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 430*x^5 - 860*x^4*y + 4200*x^4 + 8400*x^3*y - 17440*x^3 - 34880*x^2*y + 34376*x^2 + 68752*x*y - 26416*x - 52832*y

comment: Cremona label 34a2.

34

2065, -93817

5:

5*x^12 + 5*x^11 - 2665*x^10 + 39040*x^9 - 164220*x^8 - 1240560*x^7 + 20367240*x^6 - 129514280*x^5 + 489613520*x^4 - 1184341760*x^3 + 1813731200*x^2 - 1616496000*x + 644656384

comment: Cremona label 34a2.

34

4945, 347687

1:

1

comment: Cremona label 34a3.

34

4945, 347687

2:

x + 2*y

comment: Cremona label 34a3.

34

4945, 347687

3:

3*x^4 + x^3 - 618*x^2 - 4932*x - 11020

comment: Cremona label 34a3.

34

4945, 347687

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 1030*x^5 - 2060*x^4*y - 16440*x^4 - 32880*x^3*y - 110200*x^3 - 220400*x^2*y - 349684*x^2 - 699368*x*y - 432616*x - 865232*y

comment: Cremona label 34a3.

34

4945, 347687

5:

5*x^12 + 5*x^11 - 6385*x^10 - 158240*x^9 - 1231080*x^8 + 9168120*x^7 + 294731700*x^6 + 3118573420*x^5 + 19220032280*x^4 + 75260067760*x^3 + 185768006240*x^2 + 265682762880*x + 169026370624

comment: Cremona label 34a3.

34

5425, 276119

1:

1

comment: Cremona label 34a4.

34

5425, 276119

2:

x + 2*y

comment: Cremona label 34a4.

34

5425, 276119

3:

3*x^4 + x^3 - 678*x^2 - 3948*x - 13098

comment: Cremona label 34a4.

34

5425, 276119

4:

2*x^7 + 4*x^6*y + x^6 + 2*x^5*y - 1130*x^5 - 2260*x^4*y - 13160*x^4 - 26320*x^3*y - 130980*x^3 - 261960*x^2*y - 310514*x^2 - 621028*x*y + 1228292*x + 2456584*y

comment: Cremona label 34a4.

34

5425, 276119

5:

5*x^12 + 5*x^11 - 7005*x^10 - 127280*x^9 - 1434510*x^8 + 7743660*x^7 + 413386650*x^6 + 3046764070*x^5 + 2993441560*x^4 + 16104362820*x^3 + 612878391560*x^2 + 2955417501680*x + 4374286367144

comment: Cremona label 34a4.

35

-416, 1448

1:

1

comment: Cremona label 35a1.

35

-416, 1448

2:

2*y + 1

comment: Cremona label 35a1.

35

-416, 1448

3:

3*x^4 + 4*x^3 + 54*x^2 + 15*x - 76

comment: Cremona label 35a1.

35

-416, 1448

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 + 180*x^4*y + 90*x^4 + 100*x^3*y + 50*x^3 - 1520*x^2*y - 760*x^2 - 788*x*y - 394*x - 2786*y - 1393

comment: Cremona label 35a1.

35

-416, 1448

5:

5*x^12 + 20*x^11 + 574*x^10 + 1195*x^9 - 7080*x^8 - 24660*x^7 - 229215*x^6 - 329236*x^5 - 944040*x^4 - 958965*x^3 - 2906300*x^2 - 771250*x + 404151

comment: Cremona label 35a1.

35

6304, 523592

1:

1

comment: Cremona label 35a2.

35

6304, 523592

2:

2*y + 1

comment: Cremona label 35a2.

35

6304, 523592

3:

3*x^4 + 4*x^3 - 786*x^2 - 7797*x - 19760

comment: Cremona label 35a2.

35

6304, 523592

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 2620*x^4*y - 1310*x^4 - 51980*x^3*y - 25990*x^3 - 395200*x^2*y - 197600*x^2 - 1519956*x*y - 759978*x - 3155362*y - 1577681

comment: Cremona label 35a2.

35

6304, 523592

5:

5*x^12 + 20*x^11 - 8106*x^10 - 257385*x^9 - 2542620*x^8 + 13314540*x^7 + 629647305*x^6 + 8498436788*x^5 + 68550430040*x^4 + 328683095055*x^3 + 719389980360*x^2 - 297518211890*x - 2941479020481

comment: Cremona label 35a2.

35

64, -568

1:

1

comment: Cremona label 35a3.

35

64, -568

2:

2*y + 1

comment: Cremona label 35a3.

35

64, -568

3:

3*x^4 + 4*x^3 - 6*x^2 + 3*x

comment: Cremona label 35a3.

35

64, -568

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 20*x^4*y - 10*x^4 + 20*x^3*y + 10*x^3 + 4*x*y + 2*x - 2*y - 1

comment: Cremona label 35a3.

35

64, -568

5:

5*x^12 + 20*x^11 - 46*x^10 + 15*x^9 + 180*x^8 - 60*x^7 + 105*x^6 - 172*x^5 + 40*x^4 + 55*x^3 - 40*x^2 + 10*x - 1

comment: Cremona label 35a3.

36

0, -864

1:

1

comment: Cremona label 36a1.

36

0, -864

2:

2*y

comment: Cremona label 36a1.

36

0, -864

3:

3*x^4 + 12*x

comment: Cremona label 36a1.

36

0, -864

4:

4*x^6*y + 80*x^3*y - 32*y

comment: Cremona label 36a1.

36

0, -864

5:

5*x^12 + 380*x^9 - 240*x^6 - 1600*x^3 - 256

comment: Cremona label 36a1.

36

720, -19008

1:

1

comment: Cremona label 36a2.

36

720, -19008

2:

2*y

comment: Cremona label 36a2.

36

720, -19008

3:

3*x^4 - 90*x^2 + 264*x - 225

comment: Cremona label 36a2.

36

720, -19008

4:

4*x^6*y - 300*x^4*y + 1760*x^3*y - 4500*x^2*y + 5280*x*y - 1988*y

comment: Cremona label 36a2.

36

720, -19008

5:

5*x^12 - 930*x^10 + 8360*x^9 - 23625*x^8 - 79200*x^7 + 896340*x^6 - 3445200*x^5 + 7611075*x^4 - 11096800*x^3 + 11832750*x^2 - 9154200*x + 3693089

comment: Cremona label 36a2.

36

0, 23328

1:

1

comment: Cremona label 36a3.

36

0, 23328

2:

2*y

comment: Cremona label 36a3.

36

0, 23328

3:

3*x^4 - 324*x

comment: Cremona label 36a3.

36

0, 23328

4:

4*x^6*y - 2160*x^3*y - 23328*y

comment: Cremona label 36a3.

36

0, 23328

5:

5*x^12 - 10260*x^9 - 174960*x^6 + 31492800*x^3 - 136048896

comment: Cremona label 36a3.

36

6480, 513216

1:

1

comment: Cremona label 36a4.

36

6480, 513216

2:

2*y

comment: Cremona label 36a4.

36

6480, 513216

3:

3*x^4 - 810*x^2 - 7128*x - 18225

comment: Cremona label 36a4.

36

6480, 513216

4:

4*x^6*y - 2700*x^4*y - 47520*x^3*y - 364500*x^2*y - 1283040*x*y - 1449252*y

comment: Cremona label 36a4.

36

6480, 513216

5:

5*x^12 - 8370*x^10 - 225720*x^9 - 1913625*x^8 + 19245600*x^7 + 653431860*x^6 + 7534652400*x^5 + 49936263075*x^4 + 218418314400*x^3 + 698712054750*x^2 + 1621639067400*x + 1962658911249

comment: Cremona label 36a4.

37

48, -216

1:

1

comment: Cremona label 37a1.

37

48, -216

2:

2*y + 1

comment: Cremona label 37a1.

37

48, -216

3:

3*x^4 - 6*x^2 + 3*x - 1

comment: Cremona label 37a1.

37

48, -216

4:

4*x^6*y + 2*x^6 - 20*x^4*y - 10*x^4 + 20*x^3*y + 10*x^3 - 20*x^2*y - 10*x^2 + 4*x*y + 2*x + 2*y + 1

comment: Cremona label 37a1.

37

48, -216

5:

5*x^12 - 62*x^10 + 95*x^9 - 105*x^8 - 60*x^7 + 285*x^6 - 174*x^5 - 5*x^4 - 5*x^3 + 35*x^2 - 15*x + 2

comment: Cremona label 37a1.

37

1120, 36296

1:

1

comment: Cremona label 37b1.

37

1120, 36296

2:

2*y + 1

comment: Cremona label 37b1.

37

1120, 36296

3:

3*x^4 + 4*x^3 - 138*x^2 - 597*x - 728

comment: Cremona label 37b1.

37

1120, 36296

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 460*x^4*y - 230*x^4 - 3980*x^3*y - 1990*x^3 - 14560*x^2*y - 7280*x^2 - 24132*x*y - 12066*x - 12226*y - 6113

comment: Cremona label 37b1.

37

1120, 36296

5:

5*x^12 + 20*x^11 - 1410*x^10 - 20745*x^9 - 112260*x^8 + 12540*x^7 + 3705225*x^6 + 23097860*x^5 + 74433560*x^4 + 152221455*x^3 + 225698160*x^2 + 247542070*x + 143747439

comment: Cremona label 37b1.

37

89920, 26964008

1:

1

comment: Cremona label 37b2.

37

89920, 26964008

2:

2*y + 1

comment: Cremona label 37b2.

37

89920, 26964008

3:

3*x^4 + 4*x^3 - 11238*x^2 - 381993*x - 3635460

comment: Cremona label 37b2.

37

89920, 26964008

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 37460*x^4*y - 18730*x^4 - 2546620*x^3*y - 1273310*x^3 - 72709200*x^2*y - 36354600*x^2 - 983047532*x*y - 491523766*x - 5189500802*y - 2594750401

comment: Cremona label 37b2.

37

89920, 26964008

5:

5*x^12 + 20*x^11 - 116110*x^10 - 12246285*x^9 - 404642880*x^8 + 13000692180*x^7 + 1770075794625*x^6 + 79736213637980*x^5 + 2093635867285480*x^4 + 34923663561500515*x^3 + 366811707298633340*x^2 + 2226149779950936370*x + 5979144886703978039

comment: Cremona label 37b2.

37

160, -2008

1:

1

comment: Cremona label 37b3.

37

160, -2008

2:

2*y + 1

comment: Cremona label 37b3.

37

160, -2008

3:

3*x^4 + 4*x^3 - 18*x^2 + 15*x - 4

comment: Cremona label 37b3.

37

160, -2008

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 60*x^4*y - 30*x^4 + 100*x^3*y + 50*x^3 - 80*x^2*y - 40*x^2 + 28*x*y + 14*x - 2*y - 1

comment: Cremona label 37b3.

37

160, -2008

5:

5*x^12 + 20*x^11 - 170*x^10 + 235*x^9 + 480*x^8 - 2340*x^7 + 4065*x^6 - 3940*x^5 + 2520*x^4 - 1365*x^3 + 700*x^2 - 250*x + 39

comment: Cremona label 37b3.

38

-455, -77293

1:

1

comment: Cremona label 38a1.

38

-455, -77293

2:

x + 2*y + 1

comment: Cremona label 38a1.

38

-455, -77293

3:

3*x^4 + x^3 + 57*x^2 + 1083*x

comment: Cremona label 38a1.

38

-455, -77293

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 96*x^5 + 190*x^4*y + 3705*x^4 + 7220*x^3*y + 3610*x^3 - 6859*x^2 - 13718*x*y - 137180*x - 260642*y - 130321

comment: Cremona label 38a1.

38

-455, -77293

5:

5*x^12 + 5*x^11 + 590*x^10 + 34485*x^9 + 16245*x^8 + 205770*x^7 - 2057700*x^6 - 6653230*x^5 - 149217545*x^4 - 1200908015*x^3 - 470458810*x^2 - 4469358695*x - 16983563041

comment: Cremona label 38a1.

38

4105, 2115611

1:

1

comment: Cremona label 38a2.

38

4105, 2115611

2:

x + 2*y + 1

comment: Cremona label 38a2.

38

4105, 2115611

3:

3*x^4 + x^3 - 513*x^2 - 29469*x - 9766

comment: Cremona label 38a2.

38

4105, 2115611

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 854*x^5 - 1710*x^4*y - 99085*x^4 - 196460*x^3*y - 195890*x^3 - 195320*x^2*y - 1787159*x^2 - 3378998*x*y - 96510842*x - 189642686*y - 94821343

comment: Cremona label 38a2.

38

4105, 2115611

5:

5*x^12 + 5*x^11 - 5300*x^10 - 934895*x^9 - 1467465*x^8 + 49513050*x^7 - 1222214520*x^6 + 11846138810*x^5 + 982881312315*x^4 + 23694436764705*x^3 - 4412987180420*x^2 - 791688363566155*x - 9148505973767751

comment: Cremona label 38a2.

38

745, -20341

1:

1

comment: Cremona label 38a3.

38

745, -20341

2:

x + 2*y + 1

comment: Cremona label 38a3.

38

745, -20341

3:

3*x^4 + x^3 - 93*x^2 + 267*x - 218

comment: Cremona label 38a3.

38

745, -20341

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 154*x^5 - 310*x^4*y + 735*x^4 + 1780*x^3*y - 1290*x^3 - 4360*x^2*y + 361*x^2 + 5082*x*y + 1378*x - 2326*y - 1163

comment: Cremona label 38a3.

38

745, -20341

5:

5*x^12 + 5*x^11 - 960*x^10 + 8145*x^9 - 18885*x^8 - 102390*x^7 + 933000*x^6 - 3466510*x^5 + 7719635*x^4 - 11011455*x^3 + 9894360*x^2 - 5104595*x + 1148109

comment: Cremona label 38a3.

38

1, -1025

1:

1

comment: Cremona label 38b1.

38

1, -1025

2:

x + 2*y + 1

comment: Cremona label 38b1.

38

1, -1025

3:

3*x^4 + 5*x^3 + 3*x^2 + 15*x + 6

comment: Cremona label 38b1.

38

1, -1025

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 10*x^5 + 10*x^4*y + 55*x^4 + 100*x^3*y + 110*x^3 + 120*x^2*y + 85*x^2 + 50*x*y + 6*x - 38*y - 19

comment: Cremona label 38b1.

38

1, -1025

5:

5*x^12 + 25*x^11 + 56*x^10 + 525*x^9 + 1755*x^8 + 2850*x^7 + 2400*x^6 + 850*x^5 - 125*x^4 - 2875*x^3 - 3400*x^2 - 1375*x - 691

comment: Cremona label 38b1.

38

3361, 215695

1:

1

comment: Cremona label 38b2.

38

3361, 215695

2:

x + 2*y + 1

comment: Cremona label 38b2.

38

3361, 215695

3:

3*x^4 + 5*x^3 - 417*x^2 - 3345*x - 6224

comment: Cremona label 38b2.

38

3361, 215695

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 690*x^5 - 1390*x^4*y - 11845*x^4 - 22300*x^3*y - 73390*x^3 - 124480*x^2*y - 248345*x^2 - 372210*x*y - 564194*x - 756178*y - 378089

comment: Cremona label 38b2.

38

3361, 215695

5:

5*x^12 + 25*x^11 - 4284*x^10 - 112875*x^9 - 904395*x^8 + 1848750*x^7 + 97164150*x^6 + 1084824520*x^5 + 7387397375*x^4 + 28604803425*x^3 + 39626137350*x^2 - 77025287125*x - 228943289601

comment: Cremona label 38b2.

39

217, 2755

1:

1

comment: Cremona label 39a1.

39

217, 2755

2:

x + 2*y

comment: Cremona label 39a1.

39

217, 2755

3:

3*x^4 + 5*x^3 - 24*x^2 - 60*x - 41

comment: Cremona label 39a1.

39

217, 2755

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 40*x^5 - 80*x^4*y - 200*x^4 - 400*x^3*y - 410*x^3 - 820*x^2*y - 365*x^2 - 730*x*y - 72*x - 144*y

comment: Cremona label 39a1.

39

217, 2755

5:

5*x^12 + 25*x^11 - 223*x^10 - 2300*x^9 - 8805*x^8 - 13650*x^7 + 15825*x^6 + 106995*x^5 + 198375*x^4 + 205225*x^3 + 162200*x^2 + 110500*x + 40121

comment: Cremona label 39a1.

39

3337, 192763

1:

1

comment: Cremona label 39a2.

39

3337, 192763

2:

x + 2*y

comment: Cremona label 39a2.

39

3337, 192763

3:

3*x^4 + 5*x^3 - 414*x^2 - 3024*x - 6021

comment: Cremona label 39a2.

39

3337, 192763

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 690*x^5 - 1380*x^4*y - 10080*x^4 - 20160*x^3*y - 60210*x^3 - 120420*x^2*y - 169209*x^2 - 338418*x*y - 185166*x - 370332*y

comment: Cremona label 39a2.

39

3337, 192763

5:

5*x^12 + 25*x^11 - 4253*x^10 - 102660*x^9 - 859005*x^8 + 1463670*x^7 + 96703065*x^6 + 983815227*x^5 + 5527330245*x^4 + 19413317385*x^3 + 42637467690*x^2 + 53925646320*x + 30135440637

comment: Cremona label 39a2.

39

937, -25973

1:

1

comment: Cremona label 39a3.

39

937, -25973

2:

x + 2*y

comment: Cremona label 39a3.

39

937, -25973

3:

3*x^4 + 5*x^3 - 114*x^2 + 264*x - 251

comment: Cremona label 39a3.

39

937, -25973

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y - 190*x^5 - 380*x^4*y + 880*x^4 + 1760*x^3*y - 2510*x^3 - 5020*x^2*y + 2089*x^2 + 4178*x*y + 1794*x + 3588*y

comment: Cremona label 39a3.

39

937, -25973

5:

5*x^12 + 25*x^11 - 1153*x^10 + 6460*x^9 - 6555*x^8 - 213270*x^7 + 1471215*x^6 - 3572067*x^5 + 3931245*x^4 - 10476935*x^3 + 38588390*x^2 - 57716120*x + 29705987

comment: Cremona label 39a3.

39

-23, 235

1:

1

comment: Cremona label 39a4.

39

-23, 235

2:

x + 2*y

comment: Cremona label 39a4.

39

-23, 235

3:

3*x^4 + 5*x^3 + 6*x^2 - 1

comment: Cremona label 39a4.

39

-23, 235

4:

2*x^7 + 4*x^6*y + 5*x^6 + 10*x^5*y + 10*x^5 + 20*x^4*y - 10*x^3 - 20*x^2*y - 5*x^2 - 10*x*y - 2*x - 4*y

comment: Cremona label 39a4.

39

-23, 235

5:

5*x^12 + 25*x^11 + 87*x^10 + 100*x^9 - 105*x^8 - 450*x^7 - 675*x^6 - 585*x^5 - 375*x^4 - 175*x^3 - 50*x^2 + 1

comment: Cremona label 39a4.

40

336, 5184

1:

1

comment: Cremona label 40a1.

40

336, 5184

2:

2*y

comment: Cremona label 40a1.

40

336, 5184

3:

3*x^4 - 42*x^2 - 72*x - 49

comment: Cremona label 40a1.

40

336, 5184

4:

4*x^6*y - 140*x^4*y - 480*x^3*y - 980*x^2*y - 672*x*y + 220*y

comment: Cremona label 40a1.

40

336, 5184

5:

5*x^12 - 434*x^10 - 2280*x^9 - 5145*x^8 + 10080*x^7 + 94260*x^6 + 204624*x^5 + 183715*x^4 + 180960*x^3 + 416990*x^2 + 472920*x + 181009

comment: Cremona label 40a1.

40

5136, 368064

1:

1

comment: Cremona label 40a2.

40

5136, 368064

2:

2*y

comment: Cremona label 40a2.

40

5136, 368064

3:

3*x^4 - 642*x^2 - 5112*x - 11449

comment: Cremona label 40a2.

40

5136, 368064

4:

4*x^6*y - 2140*x^4*y - 34080*x^3*y - 228980*x^2*y - 729312*x*y - 907060*y

comment: Cremona label 40a2.

40

5136, 368064

5:

5*x^12 - 6634*x^10 - 161880*x^9 - 1202145*x^8 + 10939680*x^7 + 323958660*x^6 + 3394582704*x^5 + 20897479315*x^4 + 81944576160*x^3 + 202623371590*x^2 + 289886022120*x + 183853387369

comment: Cremona label 40a2.

40

96, -864

1:

1

comment: Cremona label 40a3.

40

96, -864

2:

2*y

comment: Cremona label 40a3.

40

96, -864

3:

3*x^4 - 12*x^2 + 12*x - 4

comment: Cremona label 40a3.

40

96, -864

4:

4*x^6*y - 40*x^4*y + 80*x^3*y - 80*x^2*y + 32*x*y

comment: Cremona label 40a3.

40

96, -864

5:

5*x^12 - 124*x^10 + 380*x^9 - 420*x^8 - 480*x^7 + 2160*x^6 - 2784*x^5 + 1840*x^4 - 960*x^3 + 640*x^2 - 320*x + 64

comment: Cremona label 40a3.

40

-624, 29376

1:

1

comment: Cremona label 40a4.

40

-624, 29376

2:

2*y

comment: Cremona label 40a4.

40

-624, 29376

3:

3*x^4 + 78*x^2 - 408*x - 169

comment: Cremona label 40a4.

40

-624, 29376

4:

4*x^6*y + 260*x^4*y - 2720*x^3*y - 3380*x^2*y + 7072*x*y - 45780*y

comment: Cremona label 40a4.

40

-624, 29376

5:

5*x^12 + 806*x^10 - 12920*x^9 - 17745*x^8 - 106080*x^7 - 936540*x^6 + 3999216*x^5 - 32423885*x^4 + 68862240*x^3 - 65452010*x^2 + 424116680*x - 418546631

comment: Cremona label 40a4.

42

193, -5921

1:

1

comment: Cremona label 42a1.

42

193, -5921

2:

x + 2*y + 1

comment: Cremona label 42a1.

42

193, -5921

3:

3*x^4 + 5*x^3 - 21*x^2 + 63*x + 14

comment: Cremona label 42a1.

42

193, -5921

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 30*x^5 - 70*x^4*y + 175*x^4 + 420*x^3*y + 350*x^3 + 280*x^2*y + 357*x^2 + 434*x*y - 322*x - 1078*y - 539

comment: Cremona label 42a1.

42

193, -5921

5:

5*x^12 + 25*x^11 - 192*x^10 + 1645*x^9 + 6195*x^8 + 1890*x^7 - 5040*x^6 - 78414*x^5 + 174195*x^4 - 58555*x^3 - 439040*x^2 + 375585*x - 240443

comment: Cremona label 42a1.

42

4033, -255905

1:

1

comment: Cremona label 42a2.

42

4033, -255905

2:

x + 2*y + 1

comment: Cremona label 42a2.

42

4033, -255905

3:

3*x^4 + 5*x^3 - 501*x^2 + 3135*x - 5666

comment: Cremona label 42a2.

42

4033, -255905

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 830*x^5 - 1670*x^4*y + 9615*x^4 + 20900*x^3*y - 46210*x^3 - 113320*x^2*y + 89525*x^2 + 292370*x*y + 382*x - 291606*y - 145803

comment: Cremona label 42a2.

42

4033, -255905

5:

5*x^12 + 25*x^11 - 5152*x^10 + 90925*x^9 - 359805*x^8 - 7785150*x^7 + 136516800*x^6 - 1087429470*x^5 + 5282653875*x^4 - 16621089275*x^3 + 33602934800*x^2 - 40517027375*x + 22678227221

comment: Cremona label 42a2.

42

4993, -124865

1:

1

comment: Cremona label 42a3.

42

4993, -124865

2:

x + 2*y + 1

comment: Cremona label 42a3.

42

4993, -124865

3:

3*x^4 + 5*x^3 - 621*x^2 + 1215*x - 10206

comment: Cremona label 42a3.

42

4993, -124865

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 1030*x^5 - 2070*x^4*y + 3015*x^4 + 8100*x^3*y - 98010*x^3 - 204120*x^2*y - 69255*x^2 + 65610*x*y + 1981422*x + 3897234*y + 1948617

comment: Cremona label 42a3.

42

4993, -124865

5:

5*x^12 + 25*x^11 - 6392*x^10 + 28125*x^9 - 980505*x^8 - 7107750*x^7 + 316896300*x^6 - 274315410*x^5 - 11876230125*x^4 - 10668678075*x^3 + 553389513300*x^2 - 1027740463875*x + 1382703725241

comment: Cremona label 42a3.

42

64513, -16385921

1:

1

comment: Cremona label 42a4.

42

64513, -16385921

2:

x + 2*y + 1

comment: Cremona label 42a4.

42

64513, -16385921

3:

3*x^4 + 5*x^3 - 8061*x^2 + 220863*x - 1712966

comment: Cremona label 42a4.

42

64513, -16385921

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 13430*x^5 - 26870*x^4*y + 722775*x^4 + 1472420*x^3*y - 16393450*x^3 - 34259320*x^2*y + 172125137*x^2 + 378509594*x*y - 628057202*x - 1634623998*y - 817311999

comment: Cremona label 42a4.

42

64513, -16385921

5:

5*x^12 + 25*x^11 - 83272*x^10 + 6859645*x^9 - 163296705*x^8 - 6705423510*x^7 + 623304281460*x^6 - 22261938641034*x^5 + 472256672698995*x^4 - 6403995414720155*x^3 + 54834383816877260*x^2 - 271711248903687515*x + 596401555913704337

comment: Cremona label 42a4.

42

43873, 9101359

1:

1

comment: Cremona label 42a5.

42

43873, 9101359

2:

x + 2*y + 1

comment: Cremona label 42a5.

42

43873, 9101359

3:

3*x^4 + 5*x^3 - 5481*x^2 - 130977*x - 889056

comment: Cremona label 42a5.

42

43873, 9101359

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 9130*x^5 - 18270*x^4*y - 445725*x^4 - 873180*x^3*y - 9327150*x^3 - 17781120*x^2*y - 93100833*x^2 - 168420546*x*y - 366013242*x - 563605938*y - 281802969

comment: Cremona label 42a5.

42

43873, 9101359

5:

5*x^12 + 25*x^11 - 56612*x^10 - 4238955*x^9 - 103174155*x^8 + 1992874590*x^7 + 208738402110*x^6 + 6639288840576*x^5 + 120783999373695*x^4 + 1416817295334945*x^3 + 11298066319724310*x^2 + 60154799327812035*x + 165581178470601327

comment: Cremona label 42a5.

42

-18527, -964529

1:

1

comment: Cremona label 42a6.

42

-18527, -964529

2:

x + 2*y + 1

comment: Cremona label 42a6.

42

-18527, -964529

3:

3*x^4 + 5*x^3 + 2319*x^2 + 15327*x - 142996

comment: Cremona label 42a6.

42

-18527, -964529

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 3870*x^5 + 7730*x^4*y + 54955*x^4 + 102180*x^3*y - 1378870*x^3 - 2859920*x^2*y - 6094197*x^2 - 9328474*x*y - 141302026*x - 273275578*y - 136637789

comment: Cremona label 42a6.

42

-18527, -964529

5:

5*x^12 + 25*x^11 + 23988*x^10 + 524005*x^9 - 13865055*x^8 + 54129510*x^7 - 17321732190*x^6 - 159314426556*x^5 - 3984572771505*x^4 - 13750996434895*x^3 - 486045909341390*x^2 - 3220429205292585*x - 642541689717173

comment: Cremona label 42a6.

43

16, -280

1:

1

comment: Cremona label 43a1.

43

16, -280

2:

2*y + 1

comment: Cremona label 43a1.

43

16, -280

3:

3*x^4 + 4*x^3 + 3*x + 1

comment: Cremona label 43a1.

43

16, -280

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 + 20*x^3*y + 10*x^3 + 20*x^2*y + 10*x^2 + 8*x*y + 4*x - 2*y - 1

comment: Cremona label 43a1.

43

16, -280

5:

5*x^12 + 20*x^11 + 16*x^10 + 95*x^9 + 285*x^8 + 360*x^7 + 225*x^6 + 34*x^5 + 15*x^4 - 5*x^3 - 25*x^2 - 5*x - 2

comment: Cremona label 43a1.

44

-128, 1664

1:

1

comment: Cremona label 44a1.

44

-128, 1664

2:

2*y

comment: Cremona label 44a1.

44

-128, 1664

3:

3*x^4 + 4*x^3 + 18*x^2 - 12*x - 13

comment: Cremona label 44a1.

44

-128, 1664

4:

4*x^6*y + 8*x^5*y + 60*x^4*y - 80*x^3*y - 260*x^2*y - 56*x*y - 188*y

comment: Cremona label 44a1.

44

-128, 1664

5:

5*x^12 + 20*x^11 + 202*x^10 - 140*x^9 - 2085*x^8 - 5400*x^7 - 13620*x^6 - 9016*x^5 - 22965*x^4 - 14460*x^3 - 13430*x^2 + 14660*x + 693

comment: Cremona label 44a1.

44

3712, 227456

1:

1

comment: Cremona label 44a2.

44

3712, 227456

2:

2*y

comment: Cremona label 44a2.

44

3712, 227456

3:

3*x^4 + 4*x^3 - 462*x^2 - 3468*x - 7085

comment: Cremona label 44a2.

44

3712, 227456

4:

4*x^6*y + 8*x^5*y - 1540*x^4*y - 23120*x^3*y - 141700*x^2*y - 412728*x*y - 490492*y

comment: Cremona label 44a2.

44

3712, 227456

5:

5*x^12 + 20*x^11 - 4758*x^10 - 115980*x^9 - 952005*x^8 + 2790120*x^7 + 131236620*x^6 + 1349951432*x^5 + 7855329035*x^4 + 28521769860*x^3 + 62580382890*x^2 + 71841590980*x + 27916280469

comment: Cremona label 44a2.

45

9, 4347

1:

1

comment: Cremona label 45a1.

45

9, 4347

2:

x + 2*y

comment: Cremona label 45a1.

45

9, 4347

3:

3*x^4 - 3*x^3 - 60*x + 15

comment: Cremona label 45a1.

45

9, 4347

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 200*x^4 - 400*x^3*y + 150*x^3 + 300*x^2*y - 45*x^2 - 90*x*y - 400*x - 800*y

comment: Cremona label 45a1.

45

9, 4347

5:

5*x^12 - 15*x^11 + 9*x^10 - 1900*x^9 + 4275*x^8 - 4050*x^7 - 3975*x^6 + 8595*x^5 + 3375*x^4 + 196625*x^3 - 150000*x^2 + 22500*x - 163375

comment: Cremona label 45a1.

45

2169, 99603

1:

1

comment: Cremona label 45a2.

45

2169, 99603

2:

x + 2*y

comment: Cremona label 45a2.

45

2169, 99603

3:

3*x^4 - 3*x^3 - 270*x^2 - 1248*x - 1713

comment: Cremona label 45a2.

45

2169, 99603

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 450*x^5 - 900*x^4*y - 4160*x^4 - 8320*x^3*y - 17130*x^3 - 34260*x^2*y - 32301*x^2 - 64602*x*y - 18886*x - 37772*y

comment: Cremona label 45a2.

45

2169, 99603

5:

5*x^12 - 15*x^11 - 2781*x^10 - 36820*x^9 - 123705*x^8 + 1585710*x^7 + 21983205*x^6 + 128905191*x^5 + 449276085*x^4 + 1063427465*x^3 + 1919959050*x^2 + 2568028320*x + 1758238481

comment: Cremona label 45a2.

45

34569, 6427323

1:

1

comment: Cremona label 45a3.

45

34569, 6427323

2:

x + 2*y

comment: Cremona label 45a3.

45

34569, 6427323

3:

3*x^4 - 3*x^3 - 4320*x^2 - 87108*x - 496623

comment: Cremona label 45a3.

45

34569, 6427323

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 7200*x^5 - 14400*x^4*y - 290360*x^4 - 580720*x^3*y - 4966230*x^3 - 9932460*x^2*y - 40321971*x^2 - 80643942*x*y - 127952176*x - 255904352*y

comment: Cremona label 45a3.

45

34569, 6427323

5:

5*x^12 - 15*x^11 - 44631*x^10 - 2715220*x^9 - 48225555*x^8 + 1388443410*x^7 + 96438717255*x^6 + 2539011346461*x^5 + 39628565814735*x^4 + 395124255738065*x^3 + 2486918935462800*x^2 + 9056803238629020*x + 14609207696248271

comment: Cremona label 45a3.

45

4329, -131733

1:

1

comment: Cremona label 45a4.

45

4329, -131733

2:

x + 2*y

comment: Cremona label 45a4.

45

4329, -131733

3:

3*x^4 - 3*x^3 - 540*x^2 + 2100*x - 8625

comment: Cremona label 45a4.

45

4329, -131733

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 900*x^5 - 1800*x^4*y + 7000*x^4 + 14000*x^3*y - 86250*x^3 - 172500*x^2*y + 151875*x^2 + 303750*x*y + 1062500*x + 2125000*y

comment: Cremona label 45a4.

45

4329, -131733

5:

5*x^12 - 15*x^11 - 5571*x^10 + 71900*x^9 - 1000125*x^8 - 1451250*x^7 + 218690625*x^6 - 1188433125*x^5 - 2962828125*x^4 + 6914140625*x^3 + 249051562500*x^2 - 929742187500*x + 1162244140625

comment: Cremona label 45a4.

45

58329, -14079933

1:

1

comment: Cremona label 45a5.

45

58329, -14079933

2:

x + 2*y

comment: Cremona label 45a5.

45

58329, -14079933

3:

3*x^4 - 3*x^3 - 7290*x^2 + 199200*x - 1526025

comment: Cremona label 45a5.

45

58329, -14079933

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 12150*x^5 - 24300*x^4*y + 664000*x^4 + 1328000*x^3*y - 15260250*x^3 - 30520500*x^2*y + 165930075*x^2 + 331860150*x*y - 700719250*x - 1401438500*y

comment: Cremona label 45a5.

45

58329, -14079933

5:

5*x^12 - 15*x^11 - 75321*x^10 + 6380900*x^9 - 169196625*x^8 - 4428533250*x^7 + 482634859125*x^6 - 17466755412825*x^5 + 368419927955625*x^4 - 4942615459834375*x^3 + 41944787248968750*x^2 - 207833501677500000*x + 464291085081265625

comment: Cremona label 45a5.

45

-15111, -989037

1:

1

comment: Cremona label 45a6.

45

-15111, -989037

2:

x + 2*y

comment: Cremona label 45a6.

45

-15111, -989037

3:

3*x^4 - 3*x^3 + 1890*x^2 + 12792*x - 102423

comment: Cremona label 45a6.

45

-15111, -989037

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y + 3150*x^5 + 6300*x^4*y + 42640*x^4 + 85280*x^3*y - 1024230*x^3 - 2048460*x^2*y - 2379051*x^2 - 4758102*x*y - 82708186*x - 165416372*y

comment: Cremona label 45a6.

45

-15111, -989037

5:

5*x^12 - 15*x^11 + 19539*x^10 + 386180*x^9 - 11330055*x^8 + 108243810*x^7 - 9844641645*x^6 - 64326267279*x^5 - 1930238117415*x^4 - 3283750675735*x^3 - 182578243719750*x^2 - 1334560111283880*x - 429309590602489

comment: Cremona label 45a6.

45

933129, -901389573

1:

1

comment: Cremona label 45a7.

45

933129, -901389573

2:

x + 2*y

comment: Cremona label 45a7.

45

933129, -901389573

3:

3*x^4 - 3*x^3 - 116640*x^2 + 12577620*x - 381058005

comment: Cremona label 45a7.

45

933129, -901389573

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 194400*x^5 - 388800*x^4*y + 41925400*x^4 + 83850800*x^3*y - 3810580050*x^3 - 7621160100*x^2*y + 164149129215*x^2 + 328298258430*x*y - 2761856417200*x - 5523712834400*y

comment: Cremona label 45a7.

45

933129, -901389573

5:

5*x^12 - 15*x^11 - 1205271*x^10 + 399457700*x^9 - 40577083425*x^8 - 4787292994650*x^7 + 1951282699571325*x^6 - 277336287118679265*x^5 + 23117368717657848375*x^4 - 1226600206331303620375*x^3 + 41016746352857549070000*x^2 - 792897895533090142867500*x + 6785373106715964391830125

comment: Cremona label 45a7.

45

47529, -19455093

1:

1

comment: Cremona label 45a8.

45

47529, -19455093

2:

x + 2*y

comment: Cremona label 45a8.

45

47529, -19455093

3:

3*x^4 - 3*x^3 - 5940*x^2 + 273180*x - 1048395

comment: Cremona label 45a8.

45

47529, -19455093

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 9900*x^5 - 19800*x^4*y + 910600*x^4 + 1821200*x^3*y - 10483950*x^3 - 20967900*x^2*y + 183443985*x^2 + 366887970*x*y - 6216101500*x - 12432203000*y

comment: Cremona label 45a8.

45

47529, -19455093

5:

5*x^12 - 15*x^11 - 61371*x^10 + 8710100*x^9 - 122374575*x^8 - 5125897350*x^7 + 178739481675*x^6 - 15627379816935*x^5 + 863161319644875*x^4 - 17372043881380375*x^3 - 59009984798392500*x^2 + 5103343371426817500*x - 50391114155001170125

comment: Cremona label 45a8.

46

489, 12555

1:

1

comment: Cremona label 46a1.

46

489, 12555

2:

x + 2*y

comment: Cremona label 46a1.

46

489, 12555

3:

3*x^4 - 3*x^3 - 60*x^2 - 144*x - 64

comment: Cremona label 46a1.

46

489, 12555

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 100*x^5 - 200*x^4*y - 480*x^4 - 960*x^3*y - 640*x^3 - 1280*x^2*y - 768*x^2 - 1536*x*y - 1024*x - 2048*y

comment: Cremona label 46a1.

46

489, 12555

5:

5*x^12 - 15*x^11 - 611*x^10 - 3960*x^9 - 240*x^8 + 46080*x^7 + 192000*x^6 + 703488*x^5 + 1699840*x^4 + 1474560*x^3 - 1638400*x^2 - 3932160*x - 2097152

comment: Cremona label 46a1.

46

8169, 738315

1:

1

comment: Cremona label 46a2.

46

8169, 738315

2:

x + 2*y

comment: Cremona label 46a2.

46

8169, 738315

3:

3*x^4 - 3*x^3 - 1020*x^2 - 9744*x - 26464

comment: Cremona label 46a2.

46

8169, 738315

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 1700*x^5 - 3400*x^4*y - 32480*x^4 - 64960*x^3*y - 264640*x^3 - 529280*x^2*y - 1024928*x^2 - 2049856*x*y - 1551744*x - 3103488*y

comment: Cremona label 46a2.

46

8169, 738315

5:

5*x^12 - 15*x^11 - 10531*x^10 - 298360*x^9 - 2340240*x^8 + 40274880*x^7 + 1237543200*x^6 + 15319341408*x^5 + 113414554240*x^4 + 538039541760*x^3 + 1613984972800*x^2 + 2805465456640*x + 2163755450368

comment: Cremona label 46a2.

48

208, 2240

1:

1

comment: Cremona label 48a1.

48

208, 2240

2:

2*y

comment: Cremona label 48a1.

48

208, 2240

3:

3*x^4 + 4*x^3 - 24*x^2 - 48*x - 32

comment: Cremona label 48a1.

48

208, 2240

4:

4*x^6*y + 8*x^5*y - 80*x^4*y - 320*x^3*y - 640*x^2*y - 512*x*y

comment: Cremona label 48a1.

48

208, 2240

5:

5*x^12 + 20*x^11 - 232*x^10 - 1840*x^9 - 6240*x^8 - 7680*x^7 + 19200*x^6 + 79872*x^5 + 107520*x^4 + 81920*x^3 + 81920*x^2 + 81920*x + 32768

comment: Cremona label 48a1.

48

3088, 171584

1:

1

comment: Cremona label 48a2.

48

3088, 171584

2:

2*y

comment: Cremona label 48a2.

48

3088, 171584

3:

3*x^4 + 4*x^3 - 384*x^2 - 2640*x - 4976

comment: Cremona label 48a2.

48

3088, 171584

4:

4*x^6*y + 8*x^5*y - 1280*x^4*y - 17600*x^3*y - 99520*x^2*y - 265088*x*y - 274944*y

comment: Cremona label 48a2.

48

3088, 171584

5:

5*x^12 + 20*x^11 - 3952*x^10 - 88720*x^9 - 680880*x^8 + 1587840*x^7 + 75970560*x^6 + 719021568*x^5 + 3804675840*x^4 + 12630901760*x^3 + 26271641600*x^2 + 31522304000*x + 16750309376

comment: Cremona label 48a2.

48

1168, -38080

1:

1

comment: Cremona label 48a3.

48

1168, -38080

2:

2*y

comment: Cremona label 48a3.

48

1168, -38080

3:

3*x^4 + 4*x^3 - 144*x^2 + 432*x - 432

comment: Cremona label 48a3.

48

1168, -38080

4:

4*x^6*y + 8*x^5*y - 480*x^4*y + 2880*x^3*y - 8640*x^2*y + 10368*x*y

comment: Cremona label 48a3.

48

1168, -38080

5:

5*x^12 + 20*x^11 - 1472*x^10 + 11760*x^9 - 19440*x^8 - 362880*x^7 + 3110400*x^6 - 11155968*x^5 + 22705920*x^4 - 41057280*x^3 + 89579520*x^2 - 134369280*x + 80621568

comment: Cremona label 48a3.

48

-32, 224

1:

1

comment: Cremona label 48a4.

48

-32, 224

2:

2*y

comment: Cremona label 48a4.

48

-32, 224

3:

3*x^4 + 4*x^3 + 6*x^2 - 1

comment: Cremona label 48a4.

48

-32, 224

4:

4*x^6*y + 8*x^5*y + 20*x^4*y - 20*x^2*y - 8*x*y - 4*y

comment: Cremona label 48a4.

48

-32, 224

5:

5*x^12 + 20*x^11 + 78*x^10 + 80*x^9 - 105*x^8 - 360*x^7 - 540*x^6 - 432*x^5 - 285*x^4 - 140*x^3 - 50*x^2 + 1

comment: Cremona label 48a4.

48

18448, -2505664

1:

1

comment: Cremona label 48a5.

48

18448, -2505664

2:

2*y

comment: Cremona label 48a5.

48

18448, -2505664

3:

3*x^4 + 4*x^3 - 2304*x^2 + 33264*x - 136368

comment: Cremona label 48a5.

48

18448, -2505664

4:

4*x^6*y + 8*x^5*y - 7680*x^4*y + 221760*x^3*y - 2727360*x^2*y + 15940224*x*y - 36426240*y

comment: Cremona label 48a5.

48

18448, -2505664

5:

5*x^12 + 20*x^11 - 23792*x^10 + 1022640*x^9 - 12322800*x^8 - 304560000*x^7 + 14343644160*x^6 - 268778985984*x^5 + 3006611101440*x^4 - 21536042572800*x^3 + 97485873131520*x^2 - 255498303836160*x + 296741724106752

comment: Cremona label 48a5.

48

-752, -150976

1:

1

comment: Cremona label 48a6.

48

-752, -150976

2:

2*y

comment: Cremona label 48a6.

48

-752, -150976

3:

3*x^4 + 4*x^3 + 96*x^2 + 2160*x + 464

comment: Cremona label 48a6.

48

-752, -150976

4:

4*x^6*y + 8*x^5*y + 320*x^4*y + 14400*x^3*y + 9280*x^2*y - 42368*x*y - 1007104*y

comment: Cremona label 48a6.

48

-752, -150976

5:

5*x^12 + 20*x^11 + 1008*x^10 + 69680*x^9 + 178320*x^8 + 858240*x^7 - 6819840*x^6 - 45230592*x^5 - 989026560*x^4 - 9864535040*x^3 - 11066470400*x^2 - 58784256000*x - 261141254144

comment: Cremona label 48a6.

49

105, 1323

1:

1

comment: Cremona label 49a1.

49

105, 1323

2:

x + 2*y

comment: Cremona label 49a1.

49

105, 1323

3:

3*x^4 - 3*x^3 - 12*x^2 - 12*x - 1

comment: Cremona label 49a1.

49

105, 1323

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 20*x^5 - 40*x^4*y - 40*x^4 - 80*x^3*y - 10*x^3 - 20*x^2*y - 13*x^2 - 26*x*y - 12*x - 24*y

comment: Cremona label 49a1.

49

105, 1323

5:

5*x^12 - 15*x^11 - 115*x^10 - 260*x^9 + 435*x^8 + 750*x^7 + 945*x^6 + 2475*x^5 + 2515*x^4 - 15*x^3 - 1580*x^2 - 940*x - 191

comment: Cremona label 49a1.

49

1785, 75411

1:

1

comment: Cremona label 49a2.

49

1785, 75411

2:

x + 2*y

comment: Cremona label 49a2.

49

1785, 75411

3:

3*x^4 - 3*x^3 - 222*x^2 - 936*x - 1135

comment: Cremona label 49a2.

49

1785, 75411

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 370*x^5 - 740*x^4*y - 3120*x^4 - 6240*x^3*y - 11350*x^3 - 22700*x^2*y - 19683*x^2 - 39366*x*y - 13354*x - 26708*y

comment: Cremona label 49a2.

49

1785, 75411

5:

5*x^12 - 15*x^11 - 2285*x^10 - 27420*x^9 - 77055*x^8 + 999090*x^7 + 12024075*x^6 + 64742745*x^5 + 212148505*x^4 + 448265145*x^3 + 600941210*x^2 + 468045240*x + 162203599

comment: Cremona label 49a2.

49

5145, -453789

1:

1

comment: Cremona label 49a3.

49

5145, -453789

2:

x + 2*y

comment: Cremona label 49a3.

49

5145, -453789

3:

3*x^4 - 3*x^3 - 642*x^2 + 6624*x - 13105

comment: Cremona label 49a3.

49

5145, -453789

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 1070*x^5 - 2140*x^4*y + 22080*x^4 + 44160*x^3*y - 131050*x^3 - 262100*x^2*y + 511827*x^2 + 1023654*x*y - 2070794*x - 4141588*y

comment: Cremona label 49a3.

49

5145, -453789

5:

5*x^12 - 15*x^11 - 6625*x^10 + 216180*x^9 - 1674105*x^8 - 10637010*x^7 + 324509325*x^6 - 4671331185*x^5 + 45811989505*x^4 - 223062488055*x^3 + 97628857510*x^2 + 2996354156640*x - 7845001306991

comment: Cremona label 49a3.

49

87465, -25865973

1:

1

comment: Cremona label 49a4.

49

87465, -25865973

2:

x + 2*y

comment: Cremona label 49a4.

49

87465, -25865973

3:

3*x^4 - 3*x^3 - 10932*x^2 + 364716*x - 3410863

comment: Cremona label 49a4.

49

87465, -25865973

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 18220*x^5 - 36440*x^4*y + 1215720*x^4 + 2431440*x^3*y - 34108630*x^3 - 68217260*x^2*y + 453240957*x^2 + 906481914*x*y - 2350566412*x - 4701132824*y

comment: Cremona label 49a4.

49

87465, -25865973

5:

5*x^12 - 15*x^11 - 112955*x^10 + 11658660*x^9 - 374552835*x^8 - 12369318030*x^7 + 1622285604975*x^6 - 71601632373435*x^5 + 1845510519830035*x^4 - 30241162978746735*x^3 + 312253456328968940*x^2 - 1865232025724206260*x + 4941147059701973839

comment: Cremona label 49a4.

50

25, 1475

1:

1

comment: Cremona label 50a1.

50

25, 1475

2:

x + 2*y + 1

comment: Cremona label 50a1.

50

25, 1475

3:

3*x^4 + x^3 - 3*x^2 - 21*x - 2

comment: Cremona label 50a1.

50

25, 1475

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 4*x^5 - 10*x^4*y - 75*x^4 - 140*x^3*y - 90*x^3 - 40*x^2*y - 29*x^2 - 18*x*y - 56*x - 94*y - 47

comment: Cremona label 50a1.

50

25, 1475

5:

5*x^12 + 5*x^11 - 30*x^10 - 675*x^9 - 525*x^8 + 30*x^7 - 570*x^6 + 20*x^5 + 2975*x^4 + 8925*x^3 + 1920*x^2 - 1505*x - 2295

comment: Cremona label 50a1.

50

6025, 467675

1:

1

comment: Cremona label 50a2.

50

6025, 467675

2:

x + 2*y + 1

comment: Cremona label 50a2.

50

6025, 467675

3:

3*x^4 + x^3 - 753*x^2 - 6621*x - 16302

comment: Cremona label 50a2.

50

6025, 467675

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 1254*x^5 - 2510*x^4*y - 23325*x^4 - 44140*x^3*y - 185090*x^3 - 326040*x^2*y - 733279*x^2 - 1140518*x*y - 1349306*x - 1558094*y - 779047

comment: Cremona label 50a2.

50

6025, 467675

5:

5*x^12 + 5*x^11 - 7780*x^10 - 212175*x^9 - 1811025*x^8 + 15151530*x^7 + 532153680*x^6 + 6199500770*x^5 + 42110508475*x^4 + 181727207425*x^3 + 493738766420*x^2 + 774815981245*x + 537721034705

comment: Cremona label 50a2.

50

3625, -263125

1:

1

comment: Cremona label 50a3.

50

3625, -263125

2:

x + 2*y + 1

comment: Cremona label 50a3.

50

3625, -263125

3:

3*x^4 + x^3 - 453*x^2 + 3579*x - 5402

comment: Cremona label 50a3.

50

3625, -263125

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 754*x^5 - 1510*x^4*y + 11175*x^4 + 23860*x^3*y - 42090*x^3 - 108040*x^2*y + 120721*x^2 + 349482*x*y - 432806*x - 1215094*y - 607547

comment: Cremona label 50a3.

50

3625, -263125

5:

5*x^12 + 5*x^11 - 4680*x^10 + 111825*x^9 - 513525*x^8 - 5890470*x^7 + 103627680*x^6 - 1156246630*x^5 + 8889445475*x^4 - 31653772575*x^3 - 12413347080*x^2 + 373158428245*x - 707051635395

comment: Cremona label 50a3.

50

-26375, 1941875

1:

1

comment: Cremona label 50a4.

50

-26375, 1941875

2:

x + 2*y + 1

comment: Cremona label 50a4.

50

-26375, 1941875

3:

3*x^4 + x^3 + 3297*x^2 - 26421*x - 304152

comment: Cremona label 50a4.

50

-26375, 1941875

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 5496*x^5 + 10990*x^4*y - 82575*x^4 - 176140*x^3*y - 3129590*x^3 - 6083040*x^2*y + 6333221*x^2 + 18749482*x*y - 402451556*x - 823652594*y - 411826297

comment: Cremona label 50a4.

50

-26375, 1941875

5:

5*x^12 + 5*x^11 + 34070*x^10 - 825675*x^9 - 32332275*x^8 - 317740470*x^7 - 51162284820*x^6 + 446765548370*x^5 - 16532807992025*x^4 + 42452606177425*x^3 - 2859265082053330*x^2 + 24003722432190745*x - 3805958848599145

comment: Cremona label 50a4.

50

145, -2105

1:

1

comment: Cremona label 50b1.

50

145, -2105

2:

x + 2*y + 1

comment: Cremona label 50b1.

50

145, -2105

3:

3*x^4 + 5*x^3 - 15*x^2 + 15*x

comment: Cremona label 50b1.

50

145, -2105

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 20*x^5 - 50*x^4*y + 25*x^4 + 100*x^3*y + 50*x^3 + 25*x^2 + 50*x*y - 50*y - 25

comment: Cremona label 50b1.

50

145, -2105

5:

5*x^12 + 25*x^11 - 130*x^10 + 225*x^9 + 1125*x^8 - 750*x^7 + 1500*x^6 - 5750*x^5 + 4375*x^4 + 3125*x^3 - 6250*x^2 + 3125*x - 625

comment: Cremona label 50b1.

50

-1055, 15535

1:

1

comment: Cremona label 50b2.

50

-1055, 15535

2:

x + 2*y + 1

comment: Cremona label 50b2.

50

-1055, 15535

3:

3*x^4 + 5*x^3 + 135*x^2 - 105*x - 550

comment: Cremona label 50b2.

50

-1055, 15535

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 230*x^5 + 450*x^4*y - 125*x^4 - 700*x^3*y - 5850*x^3 - 11000*x^2*y - 6675*x^2 - 2350*x*y - 27150*x - 51950*y - 25975

comment: Cremona label 50b2.

50

-1055, 15535

5:

5*x^12 + 25*x^11 + 1420*x^10 - 1075*x^9 - 65625*x^8 - 294750*x^7 - 3819000*x^6 - 2684750*x^5 - 39073125*x^4 - 41146875*x^3 - 304962500*x^2 + 257490625*x + 134555625

comment: Cremona label 50b2.

50

625, 184375

1:

1

comment: Cremona label 50b3.

50

625, 184375

2:

x + 2*y + 1

comment: Cremona label 50b3.

50

625, 184375

3:

3*x^4 + 5*x^3 - 75*x^2 - 2625*x - 1250

comment: Cremona label 50b3.

50

625, 184375

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 120*x^5 - 250*x^4*y - 8875*x^4 - 17500*x^3*y - 21250*x^3 - 25000*x^2*y - 40625*x^2 - 56250*x*y - 762500*x - 1468750*y - 734375

comment: Cremona label 50b3.

50

625, 184375

5:

5*x^12 + 25*x^11 - 750*x^10 - 84375*x^9 - 328125*x^8 + 93750*x^7 - 8906250*x^6 + 1562500*x^5 + 1162109375*x^4 + 17431640625*x^3 + 18750000000*x^2 - 73486328125*x - 560302734375

comment: Cremona label 50b3.

50

150625, 58459375

1:

1

comment: Cremona label 50b4.

50

150625, 58459375

2:

x + 2*y + 1

comment: Cremona label 50b4.

50

150625, 58459375

3:

3*x^4 + 5*x^3 - 18825*x^2 - 827625*x - 10188750

comment: Cremona label 50b4.

50

150625, 58459375

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 31370*x^5 - 62750*x^4*y - 2790125*x^4 - 5517500*x^3*y - 104646250*x^3 - 203775000*x^2*y - 1883946875*x^2 - 3564118750*x*y - 13954668750*x - 24345218750*y - 12172609375

comment: Cremona label 50b4.

50

150625, 58459375

5:

5*x^12 + 25*x^11 - 194500*x^10 - 26521875*x^9 - 1131890625*x^8 + 47348531250*x^7 + 8314901250000*x^6 + 484335997656250*x^5 + 16449417373046875*x^4 + 354935952001953125*x^3 + 4821667640820312500*x^2 + 37832811584228515625*x + 131279549488525390625

comment: Cremona label 50b4.

51

-32, 872

1:

1

comment: Cremona label 51a1.

51

-32, 872

2:

2*y + 1

comment: Cremona label 51a1.

51

-32, 872

3:

3*x^4 + 4*x^3 + 6*x^2 - 9*x - 4

comment: Cremona label 51a1.

51

-32, 872

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 + 20*x^4*y + 10*x^4 - 60*x^3*y - 30*x^3 - 80*x^2*y - 40*x^2 - 20*x*y - 10*x - 34*y - 17

comment: Cremona label 51a1.

51

-32, 872

5:

5*x^12 + 20*x^11 + 78*x^10 - 205*x^9 - 960*x^8 - 1620*x^7 - 1935*x^6 - 1380*x^5 - 1800*x^4 - 125*x^3 + 700*x^2 + 750*x - 89

comment: Cremona label 51a1.

51

2848, 152072

1:

1

comment: Cremona label 51a2.

51

2848, 152072

2:

2*y + 1

comment: Cremona label 51a2.

51

2848, 152072

3:

3*x^4 + 4*x^3 - 354*x^2 - 2349*x - 4264

comment: Cremona label 51a2.

51

2848, 152072

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 1180*x^4*y - 590*x^4 - 15660*x^3*y - 7830*x^3 - 85280*x^2*y - 42640*x^2 - 218900*x*y - 109450*x - 219874*y - 109937

comment: Cremona label 51a2.

51

2848, 152072

5:

5*x^12 + 20*x^11 - 3642*x^10 - 79105*x^9 - 588660*x^8 + 1236780*x^7 + 59709465*x^6 + 546694500*x^5 + 2793679800*x^4 + 8944073575*x^3 + 17866057600*x^2 + 20393743950*x + 10125586351

comment: Cremona label 51a2.

52

-48, 8640

1:

1

comment: Cremona label 52a1.

52

-48, 8640

2:

2*y

comment: Cremona label 52a1.

52

-48, 8640

3:

3*x^4 + 6*x^2 - 120*x - 1

comment: Cremona label 52a1.

52

-48, 8640

4:

4*x^6*y + 20*x^4*y - 800*x^3*y - 20*x^2*y + 160*x*y - 3204*y

comment: Cremona label 52a1.

52

-48, 8640

5:

5*x^12 + 62*x^10 - 3800*x^9 - 105*x^8 - 2400*x^7 - 24300*x^6 + 6960*x^5 - 192125*x^4 + 1600800*x^3 - 24050*x^2 + 641000*x - 2563199

comment: Cremona label 52a1.

52

192, 2592

1:

1

comment: Cremona label 52a2.

52

192, 2592

2:

2*y

comment: Cremona label 52a2.

52

192, 2592

3:

3*x^4 - 24*x^2 - 36*x - 16

comment: Cremona label 52a2.

52

192, 2592

4:

4*x^6*y - 80*x^4*y - 240*x^3*y - 320*x^2*y - 192*x*y - 32*y

comment: Cremona label 52a2.

52

192, 2592

5:

5*x^12 - 248*x^10 - 1140*x^9 - 1680*x^8 + 2880*x^7 + 17040*x^6 + 33408*x^5 + 37120*x^4 + 27840*x^3 + 16640*x^2 + 7680*x + 1792

comment: Cremona label 52a2.

53

-15, -297

1:

1

comment: Cremona label 53a1.

53

-15, -297

2:

x + 2*y + 1

comment: Cremona label 53a1.

53

-15, -297

3:

3*x^4 - 3*x^3 + 3*x^2 + 3*x - 1

comment: Cremona label 53a1.

53

-15, -297

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y + 2*x^5 + 10*x^4*y + 15*x^4 + 20*x^3*y - 20*x^2*y - 8*x^2 + 4*x*y - 4*y - 2

comment: Cremona label 53a1.

53

-15, -297

5:

5*x^12 - 15*x^11 + 40*x^10 + 65*x^9 - 240*x^8 + 300*x^7 - 255*x^6 + 135*x^5 - 110*x^4 + 10*x^3 + 20*x^2 - 15*x - 1

comment: Cremona label 53a1.

54

-567, -9477

1:

1

comment: Cremona label 54a1.

54

-567, -9477

2:

x + 2*y

comment: Cremona label 54a1.

54

-567, -9477

3:

3*x^4 - 3*x^3 + 72*x^2 + 96*x - 168

comment: Cremona label 54a1.

54

-567, -9477

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y + 120*x^5 + 240*x^4*y + 320*x^4 + 640*x^3*y - 1680*x^3 - 3360*x^2*y - 264*x^2 - 528*x*y - 5056*x - 10112*y

comment: Cremona label 54a1.

54

-567, -9477

5:

5*x^12 - 15*x^11 + 753*x^10 + 2320*x^9 - 21960*x^8 + 68400*x^7 - 608280*x^6 - 224712*x^5 - 4343040*x^4 + 1107520*x^3 - 14661120*x^2 - 23930880*x - 435712

comment: Cremona label 54a1.

54

5913, 602883

1:

1

comment: Cremona label 54a2.

54

5913, 602883

2:

x + 2*y

comment: Cremona label 54a2.

54

5913, 602883

3:

3*x^4 - 3*x^3 - 738*x^2 - 8004*x - 13128

comment: Cremona label 54a2.

54

5913, 602883

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 1230*x^5 - 2460*x^4*y - 26680*x^4 - 53360*x^3*y - 131280*x^3 - 262560*x^2*y - 616944*x^2 - 1233888*x*y - 3888736*x - 7777472*y

comment: Cremona label 54a2.

54

5913, 602883

5:

5*x^12 - 15*x^11 - 7617*x^10 - 246080*x^9 - 1018260*x^8 + 23234400*x^7 + 405412320*x^6 + 6732304128*x^5 + 77567736960*x^4 + 357338763520*x^3 - 653057137920*x^2 - 10462357524480*x - 25418356851712

comment: Cremona label 54a2.

54

153, -1917

1:

1

comment: Cremona label 54a3.

54

153, -1917

2:

x + 2*y

comment: Cremona label 54a3.

54

153, -1917

3:

3*x^4 - 3*x^3 - 18*x^2 + 36*x - 18

comment: Cremona label 54a3.

54

153, -1917

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 30*x^5 - 60*x^4*y + 120*x^4 + 240*x^3*y - 180*x^3 - 360*x^2*y + 126*x^2 + 252*x*y - 36*x - 72*y

comment: Cremona label 54a3.

54

153, -1917

5:

5*x^12 - 15*x^11 - 177*x^10 + 1320*x^9 - 3510*x^8 + 2700*x^7 + 8370*x^6 - 29322*x^5 + 45360*x^4 - 41580*x^3 + 22680*x^2 - 6480*x + 648

comment: Cremona label 54a3.

54

-63, 351

1:

1

comment: Cremona label 54b1.

54

-63, 351

2:

x + 2*y + 1

comment: Cremona label 54b1.

54

-63, 351

3:

3*x^4 - 3*x^3 + 9*x^2 - 9*x

comment: Cremona label 54b1.

54

-63, 351

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y + 12*x^5 + 30*x^4*y - 15*x^4 - 60*x^3*y - 30*x^3 + 9*x^2 + 18*x*y - 18*y - 9

comment: Cremona label 54b1.

54

-63, 351

5:

5*x^12 - 15*x^11 + 102*x^10 - 375*x^9 + 405*x^8 - 270*x^7 - 540*x^6 + 1458*x^5 - 2025*x^4 + 1485*x^3 - 810*x^2 + 405*x - 81

comment: Cremona label 54b1.

54

1377, 51759

1:

1

comment: Cremona label 54b2.

54

1377, 51759

2:

x + 2*y + 1

comment: Cremona label 54b2.

54

1377, 51759

3:

3*x^4 - 3*x^3 - 171*x^2 - 633*x - 654

comment: Cremona label 54b2.

54

1377, 51759

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 288*x^5 - 570*x^4*y - 2395*x^4 - 4220*x^3*y - 8650*x^3 - 13080*x^2*y - 16605*x^2 - 20130*x*y - 17308*x - 14486*y - 7243

comment: Cremona label 54b2.

54

1377, 51759

5:

5*x^12 - 15*x^11 - 1758*x^10 - 18335*x^9 - 40185*x^8 + 537390*x^7 + 5376810*x^6 + 25587720*x^5 + 75702375*x^4 + 137390425*x^3 + 126896100*x^2 + 15682575*x - 42739339

comment: Cremona label 54b2.

54

657, -22329

1:

1

comment: Cremona label 54b3.

54

657, -22329

2:

x + 2*y + 1

comment: Cremona label 54b3.

54

657, -22329

3:

3*x^4 - 3*x^3 - 81*x^2 + 351*x - 270

comment: Cremona label 54b3.

54

657, -22329

4:

2*x^7 + 4*x^6*y - x^6 - 6*x^5*y - 138*x^5 - 270*x^4*y + 1035*x^4 + 2340*x^3*y - 1530*x^3 - 5400*x^2*y + 1269*x^2 + 7938*x*y - 2430*x - 12798*y - 6399

comment: Cremona label 54b3.

54

657, -22329

5:

5*x^12 - 15*x^11 - 828*x^10 + 11925*x^9 - 44145*x^8 - 21870*x^7 + 709560*x^6 - 4372542*x^5 + 17988075*x^4 - 37787715*x^3 + 16227540*x^2 + 58425705*x - 67912911

comment: Cremona label 54b3.

55

201, -1701

1:

1

comment: Cremona label 55a1.

55

201, -1701

2:

x + 2*y

comment: Cremona label 55a1.

55

201, -1701

3:

3*x^4 - 3*x^3 - 24*x^2 + 36*x - 25

comment: Cremona label 55a1.

55

201, -1701

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 40*x^5 - 80*x^4*y + 120*x^4 + 240*x^3*y - 250*x^3 - 500*x^2*y + 171*x^2 + 342*x*y + 56*x + 112*y

comment: Cremona label 55a1.

55

201, -1701

5:

5*x^12 - 15*x^11 - 239*x^10 + 1380*x^9 - 4245*x^8 + 3870*x^7 + 20145*x^6 - 56229*x^5 + 43015*x^4 - 15135*x^3 + 50840*x^2 - 64380*x + 23689

comment: Cremona label 55a1.

55

1401, 51219

1:

1

comment: Cremona label 55a2.

55

1401, 51219

2:

x + 2*y

comment: Cremona label 55a2.

55

1401, 51219

3:

3*x^4 - 3*x^3 - 174*x^2 - 624*x - 685

comment: Cremona label 55a2.

55

1401, 51219

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 290*x^5 - 580*x^4*y - 2080*x^4 - 4160*x^3*y - 6850*x^3 - 13700*x^2*y - 10009*x^2 - 20018*x*y - 3534*x - 7068*y

comment: Cremona label 55a2.

55

1401, 51219

5:

5*x^12 - 15*x^11 - 1789*x^10 - 18020*x^9 - 43845*x^8 + 546870*x^7 + 5760945*x^6 + 25838091*x^5 + 68237365*x^4 + 129146865*x^3 + 213786490*x^2 + 274823120*x + 168524149

comment: Cremona label 55a2.

55

2841, -151389

1:

1

comment: Cremona label 55a3.

55

2841, -151389

2:

x + 2*y

comment: Cremona label 55a3.

55

2841, -151389

3:

3*x^4 - 3*x^3 - 354*x^2 + 2280*x - 4051

comment: Cremona label 55a3.

55

2841, -151389

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 590*x^5 - 1180*x^4*y + 7600*x^4 + 15200*x^3*y - 40510*x^3 - 81020*x^2*y + 101833*x^2 + 203666*x*y - 99582*x - 199164*y

comment: Cremona label 55a3.

55

2841, -151389

5:

5*x^12 - 15*x^11 - 3649*x^10 + 75740*x^9 - 527955*x^8 - 1596630*x^7 + 58456215*x^6 - 512381427*x^5 + 2541597085*x^4 - 7940142495*x^3 + 15583878550*x^2 - 17707715000*x + 8960781451

comment: Cremona label 55a3.

55

-39, -189

1:

1

comment: Cremona label 55a4.

55

-39, -189

2:

x + 2*y

comment: Cremona label 55a4.

55

-39, -189

3:

3*x^4 - 3*x^3 + 6*x^2 - 1

comment: Cremona label 55a4.

55

-39, -189

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y + 10*x^5 + 20*x^4*y - 10*x^3 - 20*x^2*y + 3*x^2 + 6*x*y - 2*x - 4*y

comment: Cremona label 55a4.

55

-39, -189

5:

5*x^12 - 15*x^11 + 71*x^10 - 60*x^9 - 105*x^8 + 270*x^7 - 435*x^6 + 303*x^5 - 215*x^4 + 105*x^3 - 50*x^2 + 1

comment: Cremona label 55a4.

56

-48, -1728

1:

1

comment: Cremona label 56a1.

56

-48, -1728

2:

2*y

comment: Cremona label 56a1.

56

-48, -1728

3:

3*x^4 + 6*x^2 + 24*x - 1

comment: Cremona label 56a1.

56

-48, -1728

4:

4*x^6*y + 20*x^4*y + 160*x^3*y - 20*x^2*y - 32*x*y - 132*y

comment: Cremona label 56a1.

56

-48, -1728

5:

5*x^12 + 62*x^10 + 760*x^9 - 105*x^8 + 480*x^7 - 1260*x^6 - 1392*x^5 - 7805*x^4 - 12960*x^3 - 1010*x^2 - 5320*x - 4223

comment: Cremona label 56a1.

56

912, -25920

1:

1

comment: Cremona label 56a2.

56

912, -25920

2:

2*y

comment: Cremona label 56a2.

56

912, -25920

3:

3*x^4 - 114*x^2 + 360*x - 361

comment: Cremona label 56a2.

56

912, -25920

4:

4*x^6*y - 380*x^4*y + 2400*x^3*y - 7220*x^2*y + 9120*x*y - 1364*y

comment: Cremona label 56a2.

56

912, -25920

5:

5*x^12 - 1178*x^10 + 11400*x^9 - 37905*x^8 - 136800*x^7 + 1841700*x^6 - 7537680*x^5 + 16541875*x^4 - 26738400*x^3 + 45828950*x^2 - 62643000*x + 37225081

comment: Cremona label 56a2.

56

2832, 119232

1:

1

comment: Cremona label 56a3.

56

2832, 119232

2:

2*y

comment: Cremona label 56a3.

56

2832, 119232

3:

3*x^4 - 354*x^2 - 1656*x - 3481

comment: Cremona label 56a3.

56

2832, 119232

4:

4*x^6*y - 1180*x^4*y - 11040*x^3*y - 69620*x^2*y - 130272*x*y + 212108*y

comment: Cremona label 56a3.

56

2832, 119232

5:

5*x^12 - 3658*x^10 - 52440*x^9 - 365505*x^8 + 1954080*x^7 + 57043140*x^6 + 334343088*x^5 + 642634195*x^4 + 1937531040*x^3 + 19836095590*x^2 + 67983583080*x + 74495611657

comment: Cremona label 56a3.

56

14352, -1719360

1:

1

comment: Cremona label 56a4.

56

14352, -1719360

2:

2*y

comment: Cremona label 56a4.

56

14352, -1719360

3:

3*x^4 - 1794*x^2 + 23880*x - 89401

comment: Cremona label 56a4.

56

14352, -1719360

4:

4*x^6*y - 5980*x^4*y + 159200*x^3*y - 1788020*x^2*y + 9520160*x*y - 19799604*y

comment: Cremona label 56a4.

56

14352, -1719360

5:

5*x^12 - 18538*x^10 + 756200*x^9 - 9387105*x^8 - 142802400*x^7 + 7068845700*x^6 - 123823961040*x^5 + 1274346857875*x^4 - 8353399279200*x^3 + 34519599050950*x^2 - 82483796759000*x + 87273666945001

comment: Cremona label 56a4.

56

16, 3520

1:

1

comment: Cremona label 56b1.

56

16, 3520

2:

2*y

comment: Cremona label 56b1.

56

16, 3520

3:

3*x^4 - 4*x^3 - 48*x + 16

comment: Cremona label 56b1.

56

16, 3520

4:

4*x^6*y - 8*x^5*y - 320*x^3*y + 320*x^2*y - 128*x*y - 512*y

comment: Cremona label 56b1.

56

16, 3520

5:

5*x^12 - 20*x^11 + 16*x^10 - 1520*x^9 + 4560*x^8 - 5760*x^7 + 6656*x^5 + 3840*x^4 + 97280*x^3 - 102400*x^2 + 20480*x - 69632

comment: Cremona label 56b1.

56

1936, 84160

1:

1

comment: Cremona label 56b2.

56

1936, 84160

2:

2*y

comment: Cremona label 56b2.

56

1936, 84160

3:

3*x^4 - 4*x^3 - 240*x^2 - 1008*x - 1264

comment: Cremona label 56b2.

56

1936, 84160

4:

4*x^6*y - 8*x^5*y - 800*x^4*y - 6720*x^3*y - 25280*x^2*y - 43648*x*y - 23552*y

comment: Cremona label 56b2.

56

1936, 84160

5:

5*x^12 - 20*x^11 - 2464*x^10 - 28720*x^9 - 72240*x^8 + 1261440*x^7 + 14784000*x^6 + 77974016*x^5 + 247811840*x^4 + 538926080*x^3 + 896614400*x^2 + 1101434880*x + 690024448

comment: Cremona label 56b2.

57

112, -1304

1:

1

comment: Cremona label 57a1.

57

112, -1304

2:

2*y + 1

comment: Cremona label 57a1.

57

112, -1304

3:

3*x^4 - 4*x^3 - 12*x^2 + 27*x - 13

comment: Cremona label 57a1.

57

112, -1304

4:

4*x^6*y + 2*x^6 - 8*x^5*y - 4*x^5 - 40*x^4*y - 20*x^4 + 180*x^3*y + 90*x^3 - 260*x^2*y - 130*x^2 + 176*x*y + 88*x - 58*y - 29

comment: Cremona label 57a1.

57

112, -1304

5:

5*x^12 - 20*x^11 - 108*x^10 + 1015*x^9 - 2985*x^8 + 3600*x^7 + 1305*x^6 - 11994*x^5 + 21735*x^4 - 21565*x^3 + 11545*x^2 - 2385*x - 152

comment: Cremona label 57a1.

57

313, -5005

1:

1

comment: Cremona label 57b1.

57

313, -5005

2:

x + 2*y + 1

comment: Cremona label 57b1.

57

313, -5005

3:

3*x^4 + x^3 - 39*x^2 + 63*x - 37

comment: Cremona label 57b1.

57

313, -5005

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 64*x^5 - 130*x^4*y + 145*x^4 + 420*x^3*y - 160*x^3 - 740*x^2*y - 134*x^2 + 472*x*y + 276*x + 80*y + 40

comment: Cremona label 57b1.

57

313, -5005

5:

5*x^12 + 5*x^11 - 402*x^10 + 1865*x^9 - 2940*x^8 - 11520*x^7 + 69075*x^6 - 135327*x^5 + 130320*x^4 - 128870*x^3 + 208570*x^2 - 198345*x + 68293

comment: Cremona label 57b1.

57

73, 539

1:

1

comment: Cremona label 57b2.

57

73, 539

2:

x + 2*y + 1

comment: Cremona label 57b2.

57

73, 539

3:

3*x^4 + x^3 - 9*x^2 - 9*x - 3

comment: Cremona label 57b2.

57

73, 539

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 14*x^5 - 30*x^4*y - 45*x^4 - 60*x^3*y - 60*x^3 - 60*x^2*y - 42*x^2 - 24*x*y - 12*x

comment: Cremona label 57b2.

57

73, 539

5:

5*x^12 + 5*x^11 - 92*x^10 - 315*x^9 - 450*x^8 + 1035*x^6 + 1509*x^5 + 990*x^4 + 450*x^3 + 270*x^2 + 135*x + 27

comment: Cremona label 57b2.

57

4873, -340165

1:

1

comment: Cremona label 57b3.

57

4873, -340165

2:

x + 2*y + 1

comment: Cremona label 57b3.

57

4873, -340165

3:

3*x^4 + x^3 - 609*x^2 + 4623*x - 9917

comment: Cremona label 57b3.

57

4873, -340165

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y - 1014*x^5 - 2030*x^4*y + 14395*x^4 + 30820*x^3*y - 83760*x^3 - 198340*x^2*y + 203736*x^2 + 605812*x*y - 58624*x - 723060*y - 361530

comment: Cremona label 57b3.

57

4873, -340165

5:

5*x^12 + 5*x^11 - 6292*x^10 + 144365*x^9 - 971940*x^8 - 10277220*x^7 + 270896025*x^6 - 2687285757*x^5 + 15787930470*x^4 - 59236288270*x^3 + 140293612220*x^2 - 192288283795*x + 116787676283

comment: Cremona label 57b3.

57

-407, -24661

1:

1

comment: Cremona label 57b4.

57

-407, -24661

2:

x + 2*y + 1

comment: Cremona label 57b4.

57

-407, -24661

3:

3*x^4 + x^3 + 51*x^2 + 351*x - 43

comment: Cremona label 57b4.

57

-407, -24661

4:

2*x^7 + 4*x^6*y + 3*x^6 + 2*x^5*y + 86*x^5 + 170*x^4*y + 1255*x^4 + 2340*x^3*y + 740*x^3 - 860*x^2*y - 2462*x^2 - 4064*x*y - 16452*x - 28840*y - 14420

comment: Cremona label 57b4.

57

-407, -24661

5:

5*x^12 + 5*x^11 + 528*x^10 + 11285*x^9 + 750*x^8 + 55800*x^7 - 345465*x^6 - 1609191*x^5 - 14542710*x^4 - 43337750*x^3 - 26486630*x^2 - 144488565*x - 197315873

comment: Cremona label 57b4.

57

-944, 33128

1:

1

comment: Cremona label 57c1.

57

-944, 33128

2:

2*y + 1

comment: Cremona label 57c1.

57

-944, 33128

3:

3*x^4 + 4*x^3 + 120*x^2 - 381*x - 527

comment: Cremona label 57c1.

57

-944, 33128

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 + 400*x^4*y + 200*x^4 - 2540*x^3*y - 1270*x^3 - 10540*x^2*y - 5270*x^2 + 5944*x*y + 2972*x - 74418*y - 37209

comment: Cremona label 57c1.

57

-944, 33128

5:

5*x^12 + 20*x^11 + 1256*x^10 - 10465*x^9 - 78195*x^8 - 342120*x^7 - 3225615*x^6 + 4524162*x^5 - 61678065*x^4 + 24001355*x^3 - 216207025*x^2 + 1121466515*x - 453780778

comment: Cremona label 57c1.

57

210736, 96740648

1:

1

comment: Cremona label 57c2.

57

210736, 96740648

2:

2*y + 1

comment: Cremona label 57c2.

57

210736, 96740648

3:

3*x^4 + 4*x^3 - 26340*x^2 - 1361181*x - 19725827

comment: Cremona label 57c2.

57

210736, 96740648

4:

4*x^6*y + 2*x^6 + 8*x^5*y + 4*x^5 - 87800*x^4*y - 43900*x^4 - 9074540*x^3*y - 4537270*x^3 - 394516540*x^2*y - 197258270*x^2 - 8125252736*x*y - 4062626368*x - 65350858938*y - 32675429469

comment: Cremona label 57c2.

57

210736, 96740648

5:

5*x^12 + 20*x^11 - 272164*x^10 - 43455265*x^9 - 2152882695*x^8 + 112410394080*x^7 + 22647133718985*x^6 + 1547129768603082*x^5 + 61779248249668935*x^4 + 1568634368975274755*x^3 + 25088485373843266775*x^2 + 231895287275336241215*x + 948650500681695885182

comment: Cremona label 57c2.

58

57, -621

1:

1

comment: Cremona label 58a1.

58

57, -621

2:

x + 2*y

comment: Cremona label 58a1.

58

57, -621

3:

3*x^4 - 3*x^3 - 6*x^2 + 12*x - 4

comment: Cremona label 58a1.

58

57, -621

4:

2*x^7 + 4*x^6*y - 3*x^6 - 6*x^5*y - 10*x^5 - 20*x^4*y + 40*x^4 + 80*x^3*y - 40*x^3 - 80*x^2*y + 20*x^2 + 40*x*y - 8*x - 16*y

comment: Cremona label 58a1.

58

57, -621

5:

5*x^12 - 15*x^11 - 53*x^10 + 440*x^9 - 960*x^8 + 840*x^7 + 60*x^6 - 1260*x^5 + 2200*x^4 - 2000*x^3 + 800*x^2 - 64

comment: Cremona label 58a1.

58

-239, -6137

1:

1

comment: Cremona label 58b1.

58

-239, -6137

2:

x + 2*y + 1

comment: Cremona label 58b1.

58

-239, -6137

3:

3*x^4 + 5*x^3 + 33*x^2 + 111*x + 16

comment: Cremona label 58b1.

58

-239, -6137

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y + 60*x^5 + 110*x^4*y + 425*x^4 + 740*x^3*y + 530*x^3 + 320*x^2*y - 167*x^2 - 654*x*y - 1520*x - 2386*y - 1193

comment: Cremona label 58b1.

58

-239, -6137

5:

5*x^12 + 25*x^11 + 366*x^10 + 4065*x^9 + 10005*x^8 + 19410*x^7 - 18660*x^6 - 213782*x^5 - 921865*x^4 - 1850955*x^3 - 1948890*x^2 - 2475115*x - 1637313

comment: Cremona label 58b1.

58

21841, 3249703

1:

1

comment: Cremona label 58b2.

58

21841, 3249703

2:

x + 2*y + 1

comment: Cremona label 58b2.

58

21841, 3249703

3:

3*x^4 + 5*x^3 - 2727*x^2 - 47409*x - 226324

comment: Cremona label 58b2.

58

21841, 3249703

4:

2*x^7 + 4*x^6*y + 7*x^6 + 10*x^5*y - 4540*x^5 - 9090*x^4*y - 162575*x^4 - 316060*x^3*y - 2421270*x^3 - 4526480*x^2*y - 17759787*x^2 - 30993094*x*y - 59502840*x - 88012586*y - 44006293

comment: Cremona label 58b2.

58

21841, 3249703

5:

5*x^12 + 25*x^11 - 28154*x^10 - 1546735*x^9 - 27319695*x^8 + 329102010*x^7 + 25951014240*x^6 + 605575850638*x^5 + 8195781071535*x^4 + 69433352123445*x^3 + 350989375111810*x^2 + 886614090970585*x + 602989902587187

comment: Cremona label 58b2.