curve #6141

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y² = x³ − 14545147879336031777303223849166993712647x + 758280519361749485272123765617611422299585672736041634634410

a-invariants

[0, 0, 0, -14545147879336031777303223849166993712647, 758280519361749485272123765617611422299585672736041634634410]

c-invariants

[698167098208129525310554744760015698207056, -655154368728551555275114933493616268866842021243939972324130240]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

410944274833632575363081262330000717967828708107875185254657430184526545937349897048961451449720632

discriminant (Δ)

-51455187294553256034617676642777950325705417957222525554545272204851309436673726255327195904959121353125472648701994281728

Faltings height

22.0837

naive height

289.2800

primes of bad reduction

2, 7, 17, 23, 37, 47, 59, 107, 163, 6457549778807, 26541623420471392315661, 28786878592719547853099, 2125716542956539518469818519

regulator

2558595294497089463483948755.18952122825045488946015389438087725255889161984608228333201222

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:43 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:55:45 UTC

Witness: 26 independent points log in to add more points →

(-113180445201814216706208108897905006780331660407/817459735808736808039905129, 8029485967917598869616434148134871061558438979670013804429272607224894/23372197947966362942698473283268125934133)
(-224578810449142718518034/1849, 68075053033777372869404480043281572/79507)
(1275656411090131133419, -45366049283508351101928731683876)
(115318272383185655447, 783898355001274335960127715732)
(918895644037962067693, -27627522357012783044964719021686)
(156936285741086816177/4, -3984037265489830243695026378513/8)
(1111553598329352951522755/11881, -602403130860894128479520216774099260/1295029)
(-930879651311261653691/25, 139656204268167472831778678378498/125)
(268121493113093299063, 4016644866771856787726996351236)
(8905812278971155294977, -840370332631557240609741563729818)
(20182938201363031233, 687705051988474848909914439386)
(185171621929365663556318/729, 72191967400699267997649009619284544/19683)
(3720921129527174484897, 226856199559993417919066531729018)
(44588150838213901009598/361, 6308825270779612138410842929306976/6859)
(-976850530594791684643169/7225, 309075169063596866405889264202454396/614125)
(-43588153663323392388843/361, -5956733167484380023051595027940338/6859)
(-112437323462061059055/4, 8560092493015430824276421592865/8)
(3543887043144593130845436013/106929, 210968169833167997869934550555733571704406/34965783)
(1026198159695631898581, -32657366202325411656265398461038)
(101444159190632089252459/1089, 16534750152548532990393735679931644/35937)
(172069044465487081317, -1830324866445452980152936250018)
(528148866019949411926777/169, -383544972431261007221089656261286958/2197)
(27674907858253737119113/324, -2174960532998844492567610258261549/5832)
(-4869902363681695697848947923245343632705402934592856142562935488167279352978231/38906684926315336488441270326950439202647090106267280591801, -6032139930899533148789817615414314528322320933290727916565188448785245615227876563461150456604244305254716236612822526/7674257052475191756048471409825395457316220676491626681472952181916906527100287495897299)
(181017935073115824883643902350563305414361623481201/344611510378030780679504787841, 2376942813401228141822104776672345648903888986243437163280417073599899627498/202299434542303557840404556166065795705352639)
(12733742661816628260218787833213190513355329350187896088906163886984290250046137598754778927/165045046691188099889324577488507436438469162431691697359214047131970729, -20703273558217701966917521195927039977799248444192477312510709244968638669604827808169685739548543703175507321426582261071830460686291812/67050765790185935540655265151819052074952674858659626760071859156712667538652479156510460069013863798710933)

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