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curve #5776

y² = x³ − 14837288114031932346279075

a-invariants: [0, 0, 0, 0, -14837288114031932346279075]
c-invariants: [0, 12819416930523589547185120800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 19783050818709243128372100
discriminant (Δ): -95102691226038686522792875502981370278159042193630000
Faltings height: 8.8444
naive height: 129.4415
primes of bad reduction: 2, 3, 5, 11, 17, 23, 31, 47, 59, 401
regulator: 1638908065.720978363547611807236950846637079176305341
submitted by: Maksym Voznyy
submitted at: 2026-10-25 02:00:39 UTC
last updated: 2026-10-25 02:00:39 UTC

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

(2317530031/9, -40384951746454/27)
(77573733361/144, 20555055764919991/1728)
(9015566761/36, -201347349613109/216)
(32044992742531980831/28495128025, -180452536727010198311974759146/4810120086260125)
(2122790353689/5776, 2589721235611804413/438976)
(249114497911/225, -123654962555152966/3375)
(88343325081489/33124, 830024123780766551463/6028568)

Commentary

Voznyy (2026), A = 1482604720630, [r, s, t] = [-46, -45, 51] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 02:00:39 UTC · history

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