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curve #5781

y² = x³ − 40700268622570827003075

a-invariants: [0, 0, 0, 0, -40700268622570827003075]
c-invariants: [0, 35165032089901194530656800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 162801074490283308012300
discriminant (Δ): -715613126090150910358661738468863501177684830000
Faltings height: 7.8613
naive height: 117.6442
primes of bad reduction: 2, 3, 5, 17, 23, 29, 53, 59, 73
regulator: 991977386.2602353730523540312588310624613925485347201
submitted by: Maksym Voznyy
submitted at: 2026-10-25 03:53:22 UTC
last updated: 2026-10-25 03:53:22 UTC

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

(31770696436969951/841754169, -2791766107850927221239526/24421813705197)
(3638802386929/576, -6941249757803622583/13824)
(2327754691/9, 112174565112764/27)
(162762613099/3969, -42037243132332932/250047)
(15575663037751/136161, 60629464875756019474/50243409)
(11321552226031/9801, 38093706163079444654/970299)
(37717781239/961, 4187701927793062/29791)

Commentary

Voznyy (2026), A = 77650946070, [r, s, t] = [-102, -17, 118] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 03:53:22 UTC · history

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