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curve #5777

y² = x³ − 1719035742262590160083675

a-invariants: [0, 0, 0, 0, -1719035742262590160083675]
c-invariants: [0, 1485246881314877898312295200]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 6876142969050360640334700
discriminant (Δ): -1276596237532159139946464878673675067338256650430000
Faltings height: 8.4852
naive height: 125.1308
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 43, 67, 307
regulator: 21170169.69528199095146219877851972355914696231877953
submitted by: Maksym Voznyy
submitted at: 2026-10-25 02:04:12 UTC
last updated: 2026-10-25 02:04:12 UTC

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

(84406522847959/570025, 531935815581631958302/430368875)
(9068537569/36, 815829914492047/216)
(9157453561/64, 563293517695091/512)
(1524655712671/1089, -1882008644505638194/35937)
(3073514761314361/15776784, -149276144065738880285459/62665386048)
(868096665782311/4575321, -22125667052991185783666/9786611619)
(225859617912497042929/1685707529104, -1813087414408550013413565962167/2188634998997120192)

Commentary

Voznyy (2026), A = -504650336190, [r, s, t] = [-43, 21, 54] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 02:04:12 UTC · history

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