curve #4138

y² + xy = x³ − x² − 124987760971398437767341x + 16379978983978125830857715978075573

a-invariants: [1, -1, 0, -124987760971398437767341, 16379978983978125830857715978075573]
c-invariants: [5999412526627125012832377, -14152301842130103361491244542499549389]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 6974578749359555576484858607771962783775859451775578325600362
discriminant (Δ): 9056083134847790323143477574570330929930678717731729147813228391056304
Faltings height: 12.1883
naive height: 171.1611
primes of bad reduction: 2, 3, 7, 29, 37, 3389, 97673, 20582746771, 841309472429783727766306558789779293
regulator: 180259040026579554.42680390349738620721897309620864711660245162082566743793
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:06:48 UTC
last updated: 2026-10-11 01:06:48 UTC

(266599420994374567343023/1707849081409, 57899564966503099497205057813065440/2231897448492107423)
(-210623674361, -182651483891290343)
(3833655231059198/29929, 257418650150534087844831/5177717)
(826869220739558/3481, 1986372217727250525017/205379)
(-9840958267666/25, 8464330438942774563/125)
(215033020439732906/877969, 17639200505767805357555791/822656953)
(2931596226974806/11449, -41802866408289494054203/1225043)
(-39506056296625046/613089, -74626089881310198510460399/480048687)
(88793008768477/361, -156092654249892164015/6859)
(144240454201, -36778526929975064)
(-2005767317191178/5041, -19987136439835163533675/357911)
(-5842144386131/16, -7390963787020112669/64)
(168574429966, -10033780210174097)
(7184405325334/81, 56429453480665177403/729)
(-78939890471171/225, 440632361089622065253/3375)
(-18047716499329754/105625, -6212123562340088995063769/34328125)
(455258181755233/2809, 2902882470903248306915/148877)
(-9956541135437/81, -126026866124428166848/729)

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