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History of Regulators of elliptic curves over $\mathbb{Q}$ of rank $2$

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2026-08-13 22:06 bmatschke how well the digits are known: assumed-bound (interval widened by a hand-chosen 4 ulps (blur_real_interval)) current
2026-08-09 09:14 flattening entries rewritten as records with named parameters
2026-08-09 08:34 data-repository import the current state of the data repository reviewed
2021-05-07 17:53 bmatschke from the data repository, 42a87287
2021-05-06 19:37 bmatschke from the data repository, 2353c35b

The first version, 2021-05-06 19:37

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+Title: Regulators of elliptic curves over $\mathbb{Q}$ of rank $2$+Definition: The regulator of an elliptic curve $E$ over $\mathbb{Q}$ is the  determinant+  of the height pairing matrix for a Mordell--Weil basis of $E(\mathbb{Q})$. This+  table lists regulators for elliptic curves over $\mathbb{Q}$ of rank $2$ for the+  first few conductors.+Parameters:+  N:+    title: conductor of $E$+    type: Z+  c4:+    display: $c_4$+    title: invariant $c_4$ of a minimal model of $E$+    type: Z+  c6:+    display: $c_6$+    title: invariant $c_6$ of a minimal model of $E$+    type: Z+Comments:+  comment-redundancy-of-N: The conductor $N$ can be deduced from $c_4$ and $c_6$.+    We display it for convenience.+  comment-E-from-c4c6: 'A model of $E/\mathbb{Q}$ is given by $E: y^2 = x^3 - 27 c_4+    x - 54 c_6$.'+Formulas:+  formula-height-pairing-matrix: For an elliptic curve $E$ over a number field $K$,  $\text{Reg}(E/K)+    = \det(\langle P_i, P_j\rangle)_{1\leq i, j \leq r}$,  where $P_1, \ldots, P_r$+    is a Mordell-Weil basis for $E(K)$ and $\langle ., .\rangle$ denotes the Néron-Tate+    height pairing.+Programs:+  program-sage:+    language: Sage+    code: "numbers = [E.regulator() for E in cremona_curves([1..100])\n          \+      \               if E.rank() == 2]"+References: {}+Links:+  LMFDB:+    title: 'LMFDB: Elliptic curves over Q'+    url: https://www.lmfdb.org/EllipticCurve/Q/+  Wiki:+    title: 'Wikipedia: Elliptic regulator'+    url: https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height#The_elliptic_and_abelian_regulators+Similar tables: ''+Keywords: ''+Tags:+- number theory+- ellptic curves+Data properties:+  type: R+  complete: unknown+  sources:+  - CITE{LMFDB}+Display properties:+  number-header: $\text{Reg}(E/\mathbb{Q})$+  group parameters:+  - - N+  - - c4+    - c6+Numbers:+  '389':+    112, -856:+      number: '0.152460177943143751624324757049455823243727077486630817840280980046053225683562463604114815503725140'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/389a1}[Curve in LMFDB]+  '433':+    1, -865:+      number: '0.224694163418166741612071133995500441366828602504245122090389587584966359518631258448840814631216698'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/433a1}[Curve in LMFDB]+  '446':+    201, -2565:+      number: '0.097343097569457050977495739432704989208172939672690410737770532960741287855658169074954584213200342'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/446d1}[Curve in LMFDB]+  '563':+    721, -19385:+      number: '0.219229003517995456286946191043342445936013182292306949635235128853549153560447475449101398631386840'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/563a1}[Curve in LMFDB]+  '571':+    208, -3160:+      number: '0.177253140262004931744091099725954374009088919514882655913976548196718651976790470684777261117528603'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/571b1}[Curve in LMFDB]+  '643':+    193, -2881:+      number: '0.229179621568847078938767135198384435021016866064609892171530795175183173739031503582080923195375860'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/643a1}[Curve in LMFDB]+  '655':+    624, -15768:+      number: '0.098953519892193760545568705755725427047086101265372005865419529735916351846002855154824787266326815'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/655a1}[Curve in LMFDB]+  '664':+    336, -8640:+      number: '0.096676050453051505257905379649666891427457895728973629521220199949436044312037223283359181516634763'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/664a1}[Curve in LMFDB]+  '681':+    16, -1880:+      number: '0.136079688950694268446478372652388595164331140664373493528811583359695674031154754984585001612486698'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/681c1}[Curve in LMFDB]+  '707':+    592, -14104:+      number: '0.112857456320488478087278063827153889463874016244353083503100770926691365424286392990203725861570382'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/707a1}[Curve in LMFDB]+  '709':+    112, 424:+      number: '0.258683172736406669969244323486181605005230011787390172859910225556676855959578648381920819636193570'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/709a1}[Curve in LMFDB]+  '718':+    217, -541:+      number: '0.169858359469645069055774099098995523894343766553729565234420766809505751647692222633430746413008187'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/718b1}[Curve in LMFDB]+  '794':+    121, -2125:+      number: '0.149049991080622738644474967893637870237969769009517053853634486911801611379808715844201288494990100'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/794a1}[Curve in LMFDB]+  '817':+    -32, -5176:+      number: '0.256256382257684208644536116867987065630725227139573629669925635266928713463553634782942338495484504'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/817a1}[Curve in LMFDB]+  '916':+    192, -864:+      number: '0.136468199155201822154232814330740898427586862674472555173324591512661733619919728412070561984240721'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/916c1}[Curve in LMFDB]+  '944':+    912, -29376:+      number: '0.117860680313585012773254230091271282413682214579722412438468899989926679430903892495474285835963653'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/944e1}[Curve in LMFDB]+  '997':+    256, 3880:+      number: '0.571019259287366988341108843169484267450998138539991220078617125871073872865666805594561140774652936'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/997b1}[Curve in LMFDB]+    1168, -39896:+      number: '0.249705466521919036772611254371171152496206072532342517379997380810018125410025742029706490229662446'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/997c1}[Curve in LMFDB]+  '1001':+    9552, -943704:+      number: '0.036010745756159607738796042557993006426482761999148425915425972607647271883794255986009072098455504'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1001c1}[Curve in LMFDB]+  '1028':+    496, -10720:+      number: '0.136468233449499324382525727079150093073730342779552373498321377077227681745457106500943872520935779'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1028a1}[Curve in LMFDB]+  '1034':+    553, -13141:+      number: '0.157767968506180973107359543279584913666690716526660799254454762192441057413416320176954506244676834'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1034a1}[Curve in LMFDB]+  '1058':+    -23, -1909:+      number: '0.206240920804397942166504422870821052526534417502716188615609792634865064001884536093243775806651663'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1058c1}[Curve in LMFDB]+    5497, -407629:+      number: '0.206240920804397942166504422870821052526534417502716188615609792634865064001884536093243775806651663'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1058c2}[Curve in LMFDB]+  '1070':+    489, -11637:+      number: '0.087830480218682013114903470511821582175090307105624784405230974189630782246623748980832233954616636'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1070a1}[Curve in LMFDB]+  '1073':+    2176, -101240:+      number: '0.250120597352093893537618103312362747335461359246749027299752475091946001205861056021279685799548511'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1073a1}[Curve in LMFDB]+  '1077':+    1297, -46169:+      number: '0.201754913467892920154827304013478993440967622882311160985229512752755930505068230450167987961203619'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1077a1}[Curve in LMFDB]+  '1088':+    1216, -40960:+      number: '0.531665631644888496256262446826464461629107272767801607632681217015058889982991317477847937297957912'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1088j1}[Curve in LMFDB]+    3136, 120320:+      number: '0.531665631644888496256262446826464461629107272767801607632681217015058889982991317477847937297957912'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1088j2}[Curve in LMFDB]+  '1094':+    313, -5869:+      number: '0.166108184146053262308266616645658547576907471248034496427979261017259031042948073488057037158104703'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1094a1}[Curve in LMFDB]+  '1102':+    1417, -63269:+      number: '0.148211786820240309352798455512901041710186012376140098711159352828310335728681638954905286576964739'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1102a1}[Curve in LMFDB]+  '1126':+    -87, -3861:+      number: '0.229392466733314908790662555365675758153012357259506672200559422031056021223492423660012623772687914'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1126a1}[Curve in LMFDB]+  '1132':+    256, -4960:+      number: '0.150224255238352118655264593305199228629798976145221243899500228388847498393971604063307201352694738'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1132a1}[Curve in LMFDB]+  '1137':+    97, -2609:+      number: '0.198423842896522924816956241281672271340135525545476537535105948826122087915500525239069427061342811'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1137a1}[Curve in LMFDB]+  '1141':+    1297, -83161:+      number: '0.123412280632018694933789038754797986949734108766143783481644239903797189552557493959473495020052132'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1141a1}[Curve in LMFDB]+  '1143':+    1872, -77976:+      number: '0.113423175235812137569712514175897826267800907964007285482149903446095590607096431287804194045204614'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1143c1}[Curve in LMFDB]+  '1147':+    448, -5336:+      number: '0.291623432988462341077612452184892597589732519047524473067448478027061221173805963698379804040471985'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1147a1}[Curve in LMFDB]+  '1171':+    129, 351:+      number: '0.336702983678594590092633836904224732983201739873214399956042130066449379473067539067820027804069843'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1171a1}[Curve in LMFDB]+  '1246':+    57, -10989:+      number: '0.127061335714561834847567415796069712437241706989515078132507832537043006564887965241739622727864187'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1246c1}[Curve in LMFDB]+  '1309':+    1072, -38744:+      number: '0.106196687003990621323341309634063359360539929848232551858932741700084050126576651929162592589920149'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1309b1}[Curve in LMFDB]+  '1324':+    -128, -2656:+      number: '0.222923629408171602803703802424723340837186482157495666134367920409924630862763371398430989350375254'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1324a1}[Curve in LMFDB]+  '1325':+    400, 2600:+      number: '0.143609349110837330741225485980242380383822124818549515559623022235990107205642596681474326492736665'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1325e1}[Curve in LMFDB]+  '1431':+    1377, 28431:+      number: '0.286131263106475144490237528912685825213087222520145589958391277678841465547110732559883601628831749'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1431a1}[Curve in LMFDB]+  '1436':+    592, -6976:+      number: '0.227823191360695029544374165181040425465440811202450137846286575537036788478483754248447212498099799'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1436a1}[Curve in LMFDB]+  '1443':+    433, -8585:+      number: '0.790463101484975738716171228728583121090221576397109804299181047621298436965987613327087364568169517'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1443c1}[Curve in LMFDB]+    -287, -34289:+      number: '0.790463101484975738716171228728583121090221576397109804299181047621298436965987613327087364568169517'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1443c2}[Curve in LMFDB]+  '1446':+    217, -5021:+      number: '0.119198913672753662863177385928975355535644897640312897615036836379284580414483828298957951445996168'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1446a1}[Curve in LMFDB]+  '1466':+    2001, -81945:+      number: '0.088731563108715038101038995139445276142482348488513172474792879837658367919208106992527947441373812'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1466b1}[Curve in LMFDB]+  '1477':+    289, -6481:+      number: '0.210823479499356295805680705901903390512702163487778340758160697033169624652168132800608358207908188'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1477a1}[Curve in LMFDB]+  '1480':+    1344, -44928:+      number: '0.081320491773692670134756758871851050581437862744509210602919837954920791620164789364983531578562492'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1480a1}[Curve in LMFDB]+  '1483':+    -80, -1432:+      number: '0.395288186152922788838107840821414308901883256770884322195134671071197746803757296886681483783344667'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1483a1}[Curve in LMFDB]+  '1525':+    385, -6625:+      number: '0.814290832163904975784704835254714683988820312710676349332247034446597925930024834557641391263646032'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1525c1}[Curve in LMFDB]+    1585, 56375:+      number: '0.814290832163904975784704835254714683988820312710676349332247034446597925930024834557641391263646032'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1525c2}[Curve in LMFDB]+  '1531':+    672, -17496:+      number: '0.489541741574875433625372407248483530236842851040701958069484747057204070193532181958946738604153774'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1531a1}[Curve in LMFDB]+  '1534':+    -231, -33021:+      number: '0.178876717887612784132978127267341419787104025981586258798611110811191745800741774633004226704306973'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1534b1}[Curve in LMFDB]+  '1570':+    169, -5653:+      number: '0.128559333075317670967751531857549209252723667027865300090710431100473425923253982450691551014996600'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1570b1}[Curve in LMFDB]+  '1576':+    448, 1664:+      number: '0.185471871948487303949609976493465442534081186614951153993413283155443888668122083574339918549039534'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1576a1}[Curve in LMFDB]+  '1591':+    3408, -477144:+      number: '0.160263038035597962822122246764595730179140373075558973376275228636532766446119003607026789106079164'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1591a1}[Curve in LMFDB]+  '1594':+    1281, -59265:+      number: '0.095723176347514116551409992777829596670096187698301413207722379645417054642976137176067609549493283'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1594a1}[Curve in LMFDB]+  '1608':+    1216, -45440:+      number: '0.091716678290306641656900940212077016791347319184708078851906639593117638584731330318002428312582338'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1608a1}[Curve in LMFDB]+  '1611':+    432, -17496:+      number: '0.133113726866794610912968221072720380423486636850863434781758126699236588736152094232137877132297847'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1611d1}[Curve in LMFDB]+  '1613':+    160, -1144:+      number: '0.490179147362384527855224242713452449219908548749926089685933403925951618783075193015170104404796916'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1613a1}[Curve in LMFDB]+  '1615':+    10321, -1045369:+      number: '0.341762769502599926793179326999853789128253747719571798104219191593204918751222039872838810019605535'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1615a1}[Curve in LMFDB]+    5761, -1974241:+      number: '0.341762769502599926793179326999853789128253747719571798104219191593204918751222039872838810019605535'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/1615a2}[Curve in LMFDB]+  '1621':+    177, -2889:+      number: 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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/2465a2}[Curve in LMFDB]+  '2466':+    1737, -85509:+      number: '0.117070042213905474895991638155842200350373250965986826867599476013012922638317146378043297056584414'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/2466d1}[Curve in LMFDB]+  '2474':+    273, -17145:+      number: '0.159488331142987078037191883028427577414070665717275282667811437134492655234763289115536725124409710'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/2474a1}[Curve in LMFDB]+  '2480':+    784, -77248:+      number: '0.608225200708054472248541416177369011134412382082001385632568723573061753967008154791072683362011702'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/2480j1}[Curve in LMFDB]+    19984, -2819008:+      number: '0.608225200708054472248541416177369011134412382082001385632568723573061753967008154791072683362011702'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/2480j2}[Curve in LMFDB]+  '2482':+    1113, 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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3324a1}[Curve in LMFDB]+  '3328':+    352, -7424:+      number: '0.382325592470181853243827781156911298796294255042349580763156767041766808814109061262371530225039429'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3328d1}[Curve in LMFDB]+    352, 573184:+      number: '0.382325592470181853243827781156911298796294255042349580763156767041766808814109061262371530225039429'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3328d2}[Curve in LMFDB]+    5664, -428544:+      number: '0.158137146843166162098213724069515529430542132745216538255315889145667510629741743534171521199505161'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3328f1}[Curve in LMFDB]+  '3333':+    10624, -1094264:+      number: '0.267181335204652773152439914412585386683869384726204190763958968628765430382542534330730466864988806'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3333a1}[Curve in LMFDB]+    2512, -125144:+      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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3663e3}[Curve in LMFDB]+    256833, -130151745:+      number: '1.765317787196908637509303909857486296189566601776684786937025006979136435807009195463508314817187627'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3663e4}[Curve in LMFDB]+  '3664':+    592, -10304:+      number: '0.500893556934910940906665279764202412202937221723772269030952312064565566962288591998747235438517612'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3664d1}[Curve in LMFDB]+    2064, -91584:+      number: '0.214415770559117383285548227523723742159141134138988971572508850121638979556480263950821975734291434'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3664e1}[Curve in LMFDB]+    1552, -46016:+      number: '0.310379570247703130741065590489865134868322666109467641496570438270492863150513478692480293066220353'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3664g1}[Curve in LMFDB]+  '3672':+    1872, -91584:+      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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3717b2}[Curve in LMFDB]+  '3718':+    1417, -71461:+      number: '0.217502353181533669506371470424665214637994626757516057375669432424807240574634814302490531199835686'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3718k1}[Curve in LMFDB]+    -11063, 845819:+      number: '0.217502353181533669506371470424665214637994626757516057375669432424807240574634814302490531199835686'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3718k2}[Curve in LMFDB]+  '3731':+    5392, -889624:+      number: '0.108671268287124703749632716596998484058752836184566002464902532379585084029328354145241127265124767'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3731c1}[Curve in LMFDB]+  '3737':+    428496, -280487448:+      number: '0.278019299088007376190495701691977311809246821667420782212798116477696611271407052242618978010157007'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3737b1}[Curve in LMFDB]+  '3742':+    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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3779a1}[Curve in LMFDB]+  '3782':+    6297, -501309:+      number: '0.250101782459176018186804396475518241421837892186049111061504174857887015223526731977485951695975726'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3782a1}[Curve in LMFDB]+  '3784':+    -9536, 470656:+      number: '0.155889921768882999243403221110278737062945098904626405305691330449930194406735869757490810764008855'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3784f1}[Curve in LMFDB]+  '3786':+    -167, -3869:+      number: '0.467226753803434746086133974722377115212734508701546498585682547615670102482574423652058820359348871'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3786a1}[Curve in LMFDB]+    9841, -1016585:+      number: '0.081963615049354946967691690136551678436771459322769947707966094070132636243909460344172225188504604'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/3786c1}[Curve in LMFDB]+  '3799':+    208, 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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4547a1}[Curve in LMFDB]+  '4554':+    -567, -2565:+      number: '1.504478017017479690544793291633555710807135437288009842294726912967540056926994251512294037616652612'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4554b1}[Curve in LMFDB]+    2313, -20709:+      number: '0.376119504254369922636198322908388927701783859322002460573681728241885014231748562878073509404163153'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4554b2}[Curve in LMFDB]+  '4564':+    -48, 22464:+      number: '0.914981722505443859839826134521580507045532407447214536384739733276545297678713644456011598837869068'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4564a1}[Curve in LMFDB]+  '4569':+    1393, -28009:+      number: '0.207382812217047142799188610527246467114059854268626805886008206049535683399972549135211064426074983'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4569b1}[Curve in LMFDB]+  '4572':+    1152, 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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4592c2}[Curve in LMFDB]+    30864, -5420736:+      number: '0.327747853987716906524306325671401868837330412899262557133164494434948299876098834529480537551360470'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4592g1}[Curve in LMFDB]+  '4593':+    -368, -12824:+      number: '0.431686363993268527537047128722955096297708399723704106459504971093517757980940479210869000581647816'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4593a1}[Curve in LMFDB]+  '4595':+    -119, -2501:+      number: '1.497328411814904484344214453619947727766665716380721397438780970435307782151624168084594165422991213'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4595a1}[Curve in LMFDB]+  '4600':+    -320, -35200:+      number: '0.198472367810723118977812822350113960600923247648052101351357024365662360044758565113037454975175323'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4600g1}[Curve in LMFDB]+  '4605':+    784, 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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4659b1}[Curve in LMFDB]+  '4662':+    3033, -370845:+      number: '0.458309268223680280361168379386359959912696211576741891749485018898053578154066843320971469484270958'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4662b1}[Curve in LMFDB]+    63513, -15992829:+      number: '0.458309268223680280361168379386359959912696211576741891749485018898053578154066843320971469484270958'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4662b2}[Curve in LMFDB]+  '4668':+    3712, -192896:+      number: '0.261410896488033981760014198389561617242989728251805615338857024652326269122970230970221211415382718'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4668a1}[Curve in LMFDB]+  '4669':+    21697, -3205889:+      number: '0.149126151830216035338877965652720458115617070310509962239550556847488157368319054496484865950428915'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4669b1}[Curve in LMFDB]+  '4675':+    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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4768a1}[Curve in LMFDB]+  '4776':+    3472, -204704:+      number: '0.236101050793103231899195098665736458262293446991663953766321817082773707374429720270051322222777948'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4776b1}[Curve in LMFDB]+  '4799':+    1489, -57529:+      number: '0.750770421053130060386610753982760827910389280692071200523453991675851190001535003102717392427876849'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4799c1}[Curve in LMFDB]+  '4806':+    8001, -599265:+      number: '0.077438591985228411950700164824870014663604906750068931605997387764898070989930638779118434477695273'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4806e1}[Curve in LMFDB]+  '4811':+    865, -28081:+      number: '0.345089716902333727651042835452208570828946149008634620451946011051493504159734414636450396918520039'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/4811a1}[Curve in LMFDB]+  '4836':+  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comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5472g2}[Curve in LMFDB]+  '5484':+    -128, -5984:+      number: '0.447168326688105378149912717006974325818166097120958806810710189884571249406125877322379339777202197'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5484a1}[Curve in LMFDB]+    21952, -3290464:+      number: '0.091438326792171664074683188436832944166798165667421425211672760527770874664678181672102216952331230'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5484d1}[Curve in LMFDB]+  '5497':+    6145, -481697:+      number: '0.703386591467760666894781932739876869333746357804865152407317565930625568628545022439873978183703397'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5497a1}[Curve in LMFDB]+  '5499':+    14832, -1729944:+      number: '0.163340266628100654461769595836989607280866671388764389223424990316346695811673819303568988809715794'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5499f1}[Curve in LMFDB]+  '5510':+    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