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19163 bytes, as of the version from 2026-09-10 23:55 (current). Recorded here, not run.
"""LMFDB genus 2 isogeny classes used by generate.py.
These are the odd-conductor classes with conductor at most 1000 from
`g2c_curves`, sorted by conductor and LMFDB class label. The leading
coefficient and BSD fields are kept for independent checks; generate.py
computes the NumberDB value from the equation and rank.
"""
CLASS_DATA = [
{
"label": "169.a",
"curve_label": "169.a.169.1",
"conductor": 169,
"rank": 0,
"equation": "[[0,0,0,0,1,1],[1,1,0,1]]",
"leading_coeff": "0.0904903908324296291135897572580154122647328643874476536",
"real_period": "32.667031090507096110005902370",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 19,
"curves_in_class": 1,
},
{
"label": "249.a",
"curve_label": "249.a.249.1",
"conductor": 249,
"rank": 0,
"equation": "[[0,1,1],[1,0,0,1]]",
"leading_coeff": "0.1315495070114787592134013430121752606933130670903651314",
"real_period": "25.783703374249836805826663230",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 14,
"curves_in_class": 2,
},
{
"label": "277.a",
"curve_label": "277.a.277.1",
"conductor": 277,
"rank": 0,
"equation": "[[0,-1,-1],[1,1,1,1]]",
"leading_coeff": "0.1431366605510114901557152099923829602231949697145570071",
"real_period": "32.205748623977585285035922248",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 15,
"curves_in_class": 2,
},
{
"label": "295.a",
"curve_label": "295.a.295.1",
"conductor": 295,
"rank": 0,
"equation": "[[0,0,-1],[1,0,0,1]]",
"leading_coeff": "0.1492683688832182090588207138996158657800381952357760759",
"real_period": "29.256600301110768975528859924",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 14,
"curves_in_class": 2,
},
{
"label": "349.a",
"curve_label": "349.a.349.1",
"conductor": 349,
"rank": 0,
"equation": "[[0,0,-1,-1],[1,1,1,1]]",
"leading_coeff": "0.1656123320984078287720952736293483346027630844236898789",
"real_period": "27.988484124630923062484101243",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 13,
"curves_in_class": 1,
},
{
"label": "353.a",
"curve_label": "353.a.353.1",
"conductor": 353,
"rank": 0,
"equation": "[[0,0,1],[1,1,0,1]]",
"leading_coeff": "0.1859131786554872680710289056816858155417289571348692034",
"real_period": "22.495494617313959436594497587",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 11,
"curves_in_class": 1,
},
{
"label": "363.a",
"curve_label": "363.a.11979.1",
"conductor": 363,
"rank": 0,
"equation": "[[0,2,4,2,0,1],[1,0,1]]",
"leading_coeff": "0.1897059599534884032426437150258731309381975729352148588",
"real_period": "18.970595995348840324264371503",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 20,
"curves_in_class": 2,
},
{
"label": "389.a",
"curve_label": "389.a.389.1",
"conductor": 389,
"rank": 0,
"equation": "[[7,16,0,-8,-2,1],[0,1,0,1]]",
"leading_coeff": "0.1979862013008733330350209978381275022945283583377101838",
"real_period": "19.798620130087333303502099784",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 2,
},
{
"label": "427.a",
"curve_label": "427.a.2989.1",
"conductor": 427,
"rank": 0,
"equation": "[[-4,4,4,-5,-1,1],[1,0,0,1]]",
"leading_coeff": "0.1899303686308920817263923619718777416326660023276608068",
"real_period": "18.613176125827424009186451473",
"regulator": "1.0",
"tamagawa_product": 2,
"analytic_sha": 1,
"torsion_order": 14,
"curves_in_class": 1,
},
{
"label": "461.a",
"curve_label": "461.a.461.1",
"conductor": 461,
"rank": 0,
"equation": "[[-2,3,0,-3,0,1],[0,0,0,1]]",
"leading_coeff": "0.2458864264726567276756390789225886309416527367578934646",
"real_period": "12.048434897160179656106314867",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 7,
"curves_in_class": 2,
},
{
"label": "523.a",
"curve_label": "523.a.523.1",
"conductor": 523,
"rank": 0,
"equation": "[[0,0,0,-1,-1,1],[1,1]]",
"leading_coeff": "0.2481990412677571630041171344077874577286868196753029986",
"real_period": "24.819904126775716300411713441",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 2,
},
{
"label": "529.a",
"curve_label": "529.a.529.1",
"conductor": 529,
"rank": 0,
"equation": "[[0,0,0,0,0,-1],[1,1,0,1]]",
"leading_coeff": "0.2484318665905996812072503393142383906699109867831601343",
"real_period": "30.060255857462561426077291057",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 11,
"curves_in_class": 1,
},
{
"label": "555.a",
"curve_label": "555.a.8325.1",
"conductor": 555,
"rank": 0,
"equation": "[[0,1,1,-4,-2,3],[1,1]]",
"leading_coeff": "0.2569247202971451430840301627276747947596854072417931968",
"real_period": "25.692472029714514308403016273",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 20,
"curves_in_class": 1,
},
{
"label": "587.a",
"curve_label": "587.a.587.1",
"conductor": 587,
"rank": 1,
"equation": "[[0,-1,-1],[1,1,0,1]]",
"leading_coeff": "0.11135151106422023731910273620872358675238584539624",
"real_period": "29.510964061093545829670229541",
"regulator": "0.0037732251252",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "597.a",
"curve_label": "597.a.597.1",
"conductor": 597,
"rank": 0,
"equation": "[[0,1,2,3,2,1],[1]]",
"leading_coeff": "0.2941146301882136359236849987869052563808417892096687406",
"real_period": "14.411616879222468160260564941",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 7,
"curves_in_class": 1,
},
{
"label": "603.a",
"curve_label": "603.a.603.1",
"conductor": 603,
"rank": 0,
"equation": "[[0,2,4,4,8,1],[1,0,1]]",
"leading_coeff": "0.2691001556363177690790850827729359332811643126537782509",
"real_period": "26.910015563631776907908508277",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 2,
},
{
"label": "691.a",
"curve_label": "691.a.691.1",
"conductor": 691,
"rank": 0,
"equation": "[[0,0,-1,-1,0,1],[1,1]]",
"leading_coeff": "0.2939463892598192424091021283086475110620279370319154963",
"real_period": "18.812568912628431514182536212",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 8,
"curves_in_class": 1,
},
{
"label": "709.a",
"curve_label": "709.a.709.1",
"conductor": 709,
"rank": 0,
"equation": "[[0,1,-2,0,0,1],[0,1]]",
"leading_coeff": "0.2868931505071272731308297049624563478403972027713468240",
"real_period": "18.361161632456145480373101118",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 8,
"curves_in_class": 1,
},
{
"label": "713.a",
"curve_label": "713.a.713.1",
"conductor": 713,
"rank": 1,
"equation": "[[0,-1,0,0,0,-1],[1,1,0,1]]",
"leading_coeff": "0.12839499124728345901705434747732485757963321710370",
"real_period": "27.957888812357838995963126226",
"regulator": "0.00459244230167",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "713.b",
"curve_label": "713.b.713.1",
"conductor": 713,
"rank": 0,
"equation": "[[0,0,0,0,-1],[1,1,0,1]]",
"leading_coeff": "0.2858010009469617170226097264141850097688609131635517430",
"real_period": "23.149881076703899078831387840",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 9,
"curves_in_class": 1,
},
{
"label": "731.a",
"curve_label": "731.a.12427.1",
"conductor": 731,
"rank": 0,
"equation": "[[-3,-1,0,0,2,1],[0,0,1,1]]",
"leading_coeff": "0.2985355886872414062863189873478987786819489163265650277",
"real_period": "14.926779434362070314315949367",
"regulator": "1.0",
"tamagawa_product": 2,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 1,
},
{
"label": "741.a",
"curve_label": "741.a.28899.1",
"conductor": 741,
"rank": 0,
"equation": "[[0,1,2,0,-1,-3],[1,1]]",
"leading_coeff": "0.2930756651264371996923859602312386579242554450757708092",
"real_period": "18.756842568091980780312701455",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 16,
"curves_in_class": 1,
},
{
"label": "743.a",
"curve_label": "743.a.743.1",
"conductor": 743,
"rank": 1,
"equation": "[[0,0,1,0,-1],[1,1,0,1]]",
"leading_coeff": "0.13165575038462151162891693537315062512814793312980",
"real_period": "28.765390617361029929781074294",
"regulator": "0.00457688032594",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "745.a",
"curve_label": "745.a.745.1",
"conductor": 745,
"rank": 0,
"equation": "[[0,-1],[1,1,0,1]]",
"leading_coeff": "0.3033683921052660240631287058786037771056412979842315750",
"real_period": "24.572839760526547949113425176",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 9,
"curves_in_class": 1,
},
{
"label": "763.a",
"curve_label": "763.a.763.1",
"conductor": 763,
"rank": 0,
"equation": "[[0,-1,2,0,-2],[0,1,0,1]]",
"leading_coeff": "0.3048575004522535920085251501905636550504464087246596634",
"real_period": "30.485750045225359200852515019",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 1,
},
{
"label": "797.a",
"curve_label": "797.a.797.1",
"conductor": 797,
"rank": 0,
"equation": "[[0,0,0,1,-1,1],[1]]",
"leading_coeff": "0.3559385607403319429724872658598941145484758157708627026",
"real_period": "17.440989476276265205651876027",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 7,
"curves_in_class": 1,
},
{
"label": "807.a",
"curve_label": "807.a.2421.1",
"conductor": 807,
"rank": 0,
"equation": "[[-1,2,-1,-2,0,1],[0,1,0,1]]",
"leading_coeff": "0.3050356332174254142944032925074203061350748144483253973",
"real_period": "9.7611402629576132574209053602",
"regulator": "1.0",
"tamagawa_product": 2,
"analytic_sha": 1,
"torsion_order": 8,
"curves_in_class": 1,
},
{
"label": "841.a",
"curve_label": "841.a.841.1",
"conductor": 841,
"rank": 0,
"equation": "[[2,1,3,1,1],[0,1,1,1]]",
"leading_coeff": "0.2915215656991529771681413103312969859954128318994299461",
"real_period": "14.284556719258495881238924206",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 7,
"curves_in_class": 1,
},
{
"label": "847.a",
"curve_label": "847.a.847.1",
"conductor": 847,
"rank": 1,
"equation": "[[0,0,1,1,1],[1,1,1,1]]",
"leading_coeff": "0.15924418888031945139555844635365598696887956854302",
"real_period": "20.305961378982547409515071059",
"regulator": "0.196055958529",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 5,
"curves_in_class": 1,
},
{
"label": "847.b",
"curve_label": "847.b.9317.1",
"conductor": 847,
"rank": 0,
"equation": "[[0,-1,2,-3,2,1],[1,0,1]]",
"leading_coeff": "0.3365454249762917676170118858324423791181104282638755880",
"real_period": "16.827271248814588380850594292",
"regulator": "1.0",
"tamagawa_product": 2,
"analytic_sha": 1,
"torsion_order": 10,
"curves_in_class": 1,
},
{
"label": "847.c",
"curve_label": "847.c.9317.1",
"conductor": 847,
"rank": 0,
"equation": "[[-2,-1,0,1,1],[0,0,1,1]]",
"leading_coeff": "0.3119812484526625370039160119138202568854416763558487764",
"real_period": "9.9833999504852011841253123812",
"regulator": "1.0",
"tamagawa_product": 2,
"analytic_sha": 1,
"torsion_order": 8,
"curves_in_class": 1,
},
{
"label": "847.d",
"curve_label": "847.d.456533.1",
"conductor": 847,
"rank": 0,
"equation": "[[4,-24,37,3,-22,-9,-1],[1]]",
"leading_coeff": "0.2621188089061351721920136796692074600709651668880792248",
"real_period": "9.8294553339800689572005129876",
"regulator": "1.0",
"tamagawa_product": 3,
"analytic_sha": 2,
"torsion_order": 15,
"curves_in_class": 2,
},
{
"label": "893.a",
"curve_label": "893.a.893.1",
"conductor": 893,
"rank": 1,
"equation": "[[0,0,-1,0,-1],[1,1,0,1]]",
"leading_coeff": "0.15045853782009665826690182640447906174016729630305",
"real_period": "23.402434810371670423150488330",
"regulator": "0.006429183076",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "909.a",
"curve_label": "909.a.8181.1",
"conductor": 909,
"rank": 0,
"equation": "[[0,-3,6,1,-7,3],[0,1]]",
"leading_coeff": "0.3407116942606920617569877403142908280531470474710720939",
"real_period": "21.805548432684291952447215380",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 16,
"curves_in_class": 2,
},
{
"label": "925.a",
"curve_label": "925.a.23125.1",
"conductor": 925,
"rank": 0,
"equation": "[[0,-5,18,-19,1,5],[0,1]]",
"leading_coeff": "0.3262333436965224143091586365531384380133010837975704169",
"real_period": "20.878933996577434515786152739",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 16,
"curves_in_class": 2,
},
{
"label": "953.a",
"curve_label": "953.a.953.1",
"conductor": 953,
"rank": 1,
"equation": "[[0,0,1,1],[1,1,0,1]]",
"leading_coeff": "0.15619357934555552660410512970463585348145731895332",
"real_period": "24.886681715340928998544708518",
"regulator": "0.00627619146386",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "961.a",
"curve_label": "961.a.923521.1",
"conductor": 961,
"rank": 0,
"equation": "[[-3,-2,3,4,-5],[1,0,1,1]]",
"leading_coeff": "0.4492877238760407861133296681879239133411135692122511868",
"real_period": "2.2464386193802039305666483409",
"regulator": "1.0",
"tamagawa_product": 5,
"analytic_sha": 1,
"torsion_order": 5,
"curves_in_class": 4,
},
{
"label": "971.a",
"curve_label": "971.a.971.1",
"conductor": 971,
"rank": 1,
"equation": "[[0,1,0,-2,0,1],[1]]",
"leading_coeff": "0.17699813379517644002265008924723791757417505866146",
"real_period": "29.647110801124988563042819482",
"regulator": "0.00597016468089",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 1,
"curves_in_class": 1,
},
{
"label": "975.a",
"curve_label": "975.a.63375.1",
"conductor": 975,
"rank": 0,
"equation": "[[-1,1,2,1,0,-1],[1,0,0,1]]",
"leading_coeff": "0.3987858446601027745461990966212669516993638830395369886",
"real_period": "14.356290407763699883663167478",
"regulator": "1.0",
"tamagawa_product": 4,
"analytic_sha": 1,
"torsion_order": 12,
"curves_in_class": 1,
},
{
"label": "997.a",
"curve_label": "997.a.997.1",
"conductor": 997,
"rank": 0,
"equation": "[[0,-1,0,16,-8,1],[0,1]]",
"leading_coeff": "0.3373378289933834996066688066442920811664838186274513923",
"real_period": "21.589621055576543974826803625",
"regulator": "1.0",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 8,
"curves_in_class": 2,
},
{
"label": "997.b",
"curve_label": "997.b.997.1",
"conductor": 997,
"rank": 1,
"equation": "[[0,0,-1,2,-2,1],[1]]",
"leading_coeff": "0.17999248594923943966607409206298923285358491090985",
"real_period": "19.932843365455444415240848640",
"regulator": "0.0812695080096",
"tamagawa_product": 1,
"analytic_sha": 1,
"torsion_order": 3,
"curves_in_class": 1,
},
]