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curve #5775

y² + y = x³ − 114215096576412185658019

a-invariants: [0, 0, 1, 0, -114215096576412185658019]
c-invariants: [0, 98681843442020128408528200]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 456860386305648742632075
discriminant (Δ): -5635478139534358231644810940530647383168107751875
Faltings height: 8.0333
naive height: 119.7079
primes of bad reduction: 3, 5, 7, 17, 29, 31, 103, 787
regulator: 200189844.5712020457674876853865511183656597081203220
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:57:45 UTC
last updated: 2026-10-25 01:57:45 UTC

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

(301661329/4, 4487903881213/8)
(223928575556538288289/900206259264, -3338466112590293960863215602831/854108497139609088)
(67749237438293341/1387935025, 2364959941806665040249639/51707519356375)
(336107689/4, 5537126915833/8)
(34001928121/100, 6260708586594081/1000)
(159978036780499/167281, 2023308877537628212991/68417929)
(8542221076886161/70157376, -764121292430091287037497/587638181376)

Commentary

Voznyy (2026), A = 130079802615, [r, s, t] = [-35, -31, 40] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:57:46 UTC · history

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