curve #6239

y² = x³ − 3218271920027172717806209203x + 70281615509986690284220185968865842929602

a-invariants: [0, 0, 0, -3218271920027172717806209203, 70281615509986690284220185968865842929602]
c-invariants: [154477052161304290454698041744, -60723315800628500405566240677100088291176128]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 319826371121651301614376649624178830249191682872012656626149875545301520
discriminant (Δ): -584794383213058070192774634095844552001205452695062878638930478181749956849331200
Faltings height: 14.5081
naive height: 201.6298
primes of bad reduction: 2, 3, 5, 11, 53, 2957, 159624603527999448353, 1614217544093424642173795559004876532839487
regulator: 332002179564839900353.57336877096816103547834782160505573140905566260318769670744
submitted by: apkorte
submitted at: 2026-10-31 15:39:59 UTC
last updated: 2026-10-31 15:39:59 UTC

(32517607812834, -3880898128422780498)
(32531132871651, 3802089179602944270)
(32043103215597, -7667314801418955672)
(23567198349531, -86749566846697189710)
(37099238134851, 44134389248834231730)
(18104082082626, 133983246727948239270)
(25563770410146, 68677052323218529410)
(114074538471147, -1089775544794370717778)
(33015855352371, 4054582812314478510)
(13668277044973, 169843797018325853720)
(32970689257122, -3781391348523885822)
(33885298138869, -11707536425946703848)
(48315761828973, 166064116421472972120)
(28440941827299, 41909951711275817202)
(34161417300702, 14399393495692288752)
(35982984553506, -32687335934839585890)
(37350952027467, -46735106606029943442)
(33000546313131, 3958383436131079890)
(679410147169086/25, 6722022299961340797084/125)
(32637360696117, 3308014751102147592)
(3175684750499234229/72361, -2267488983710990236151812968/19465109)

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