curve #4390

y² + xy = x³ − x² − 181329361526995810857775362240x + 29721467947304654246847689122710693363390000

a-invariants: [1, -1, 0, -181329361526995810857775362240, 29721467947304654246847689122710693363390000]
c-invariants: [8703809353295798921173217387529, -25679348306471182102134313570926893786490716133]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 488442904773890620855613130
discriminant (Δ): -35046756542843482843992776677563900554757066311287791628566336043935891404464575375600
Faltings height: 15.4822
naive height: 213.7240
primes of bad reduction: 2, 3, 5, 7, 13, 19, 31, 41, 67, 73, 109, 271, 1621, 2857, 3691
regulator: 38150415333.2359640668087077163116679191271951047531835
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:21 UTC
last updated: 2026-10-17 10:21:21 UTC

(2700917992416873, 138719316171390906720063)
(1404273538287628396/10201, 2796715063346872050095633080/1030301)
(3001671575728309147656/12187081, 1654719606289489189965858873060/42545099771)
(44431636549939174792/182329, 5395995848841449244270293604/77854483)
(150470635277224776/625, 2232084066269494220835276/15625)
(745657333089902095432/7569, 20361271211197886366030008480244/658503)
(-175956634589550138047/361201, -339896114698740068804528255577/217081801)
(16244616026767215156748/65918161, 21519730976391917861229300135336/535189549159)

2-ISOG#1 dujella/z6old678.html#pre124 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:21 UTC · history