curve #4540

y² + xy + y = x³ + x² − 331198317906888514445820524634641913x + 73454246783882868736700940050928100187028725583785031

a-invariants: [1, 1, 1, -331198317906888514445820524634641913, 73454246783882868736700940050928100187028725583785031]
c-invariants: [15897519259530648693399385182462811825, -63464469221274798707741006650481743762088207772861355625]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 730637583884344817008831385823517679172905278434785157204323102296776562143815986650 ★ record for rank ≥ 25
discriminant (Δ): -5752909721225547895619108203380932221377221679041109950928047157296313926236090850668140730568001024000000
Faltings height: 19.1962
naive height: 256.9802
primes of bad reduction: 2, 3, 5, 7, 17, 23, 47, 79, 139, 1171253, 2944052065781743598432410270337612217972426832811497940715759876593
regulator: 2329571814971474684797842.982910736397572421388498188824846921597762722219189959632816494
submitted by: Matej Jurasić
submitted at: 2026-10-17 12:07:36 UTC
last updated: 2026-10-17 12:07:36 UTC

(-80537910163846145, 315603976066765554036942872)
(372107012945337135, -41669142662403494221126968)
(458055995449263565, 133618955688606164118567842)
(1348903893116352295/4, 85927221624557587272764851/8)
(-624324159471580445, 192041344120348274018245472)
(303721750855261435, -29656438877049861426840268)
(72079949707782055, 223508347559483268069517472)
(216370649727857055, 109189357086809225725970472)
(2930301395478984535/9, -313502332180745176571993416/27)
(355735253727014515, -25549194226782292439828608)
(-333689007098434865, -383165451213294224932318168)
(444119826970555755, -118159963400732343081083728)
(12544882754675052735/49, -25303705301069749909583975944/343)
(331656709716604815, 9543125893746896455315592)
(190266703699837615, 131628868847297990686272392)
(1672044094648204015, -2047989825957756111257956408)
(-118560477626411985, 333248738830579290604987592)
(484151828681425135, -163066285312803381014246968)
(-87997029320357685, 319244908990230852256820592)
(522619233141617035, 207622440605090524262777732)
(44881097856466063655/121, -53865247627250369530662903768/1331)
(4940355155440657031/25, -15673355420211689771654221944/125)
(21977430229413608791/25, 84933385343341463063533200424/125)
(775262722207152827015/2401, -1567174186977786681718522859592/117649)
(91458549965870049169, -874637089895172962939190345658)

Specialization at T = 149/100 of a rank-17 fibration of X1152 (one neighbour step from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-17 12:07:36 UTC · history