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curve #5780

y² = x³ − 3232456909538760984494700

a-invariants: [0, 0, 0, 0, -3232456909538760984494700]
c-invariants: [0, 2792842769841489490603420800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 3232456909538760984494700
discriminant (Δ): -4513871954314747129485311932109024897487789734880000
Faltings height: 8.5905
naive height: 126.3937
primes of bad reduction: 2, 3, 5, 11, 13, 17, 59, 97, 829
regulator: 73899326.03060360847082848045889778774166897240339200
submitted by: Maksym Voznyy
submitted at: 2026-10-25 03:50:34 UTC
last updated: 2026-10-25 03:50:34 UTC

Witness: 7 independent points log in to add more points →

(4834353430930741/603729, 336129190426584504392689/469097433)
(2309166807181/3481, 3489514443626577821/205379)
(3952540189/25, 106026940747637/125)
(6731153717161/11236, 17331840858892719509/1191016)
(2605226807329/16, -4205022339346330033/64)
(102606068608861/494209, 830697005096924162491/347428927)
(2099769573790091610289/13031681243364, -45871519982399340405031961636887/47043613451031924888)

Commentary

Voznyy (2026), A = 692013370620, [r, s, t] = [-65, -44, 85] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 03:50:34 UTC · history

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