curve #1952

y² + xy = x³ − 2929637761621563858438581355x + 56324115934467582250341538214216651615025

a-invariants: [1, 0, 0, -2929637761621563858438581355, 56324115934467582250341538214216651615025]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 15205045720581255547697746106009897125859146740373110
discriminant (Δ): 238764036539896633102938109969096111058846584849866188364395093866591100338176000000
Faltings height: 14.7398
naive height: 201.3476
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 31, 53, 89, 113, 4861, 5737, 57831214471701864422747462183089
regulator: 52634036261767.4609265038205892132088285711109060314572372397139778569031
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:26 UTC
last updated: 2026-09-25 20:06:26 UTC

(146555431249902, -1665761101754485817919)
(-4752161888974770/169, 749784628174065800685045/2197)
(753377630319285/16, -9658179775514081500995/64)
(38181541373286, 11323887980586151497)
(-875074710628362/49, 110053220537110829241831/343)
(21725848453830, 54130588149864750225)
(183475048772874/25, -23458335964465904960103/125)
(24325571821689150/2209, 16546086778273585432576815/103823)
(-32757667041810, -342258827900250127935)
(15087840644299470/361, 569228435502849474320715/6859)
(23364620453310, -25082199000377244255)
(-61790624907330, -37770762974334242655)
(75888250837710, -520616486947416077055)
(1434797856911310, 54310147162445054130945)
(69990063328799316021969564726373343916038751432249123/3904108577216728329206068964224324, -18516315825376276609498755111155611768123090108389562113887610932441244022770519/243939894130731913602211037452818366995958253946168)
(249568748854420593048578334/6508340811025, 318846194073458037528267291301579735833/16603721118342373625)
(20230036237508790/529, 178814676697295309089815/12167)

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