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curve #4699

y² = x³ + 35470887868736225

a-invariants: [0, 0, 0, 0, 35470887868736225]
c-invariants: [0, -30646847118588098400]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1811784796122900519742721223240900
discriminant (Δ): -543535438836870155922816366972270000
Faltings height: 5.5358
naive height: 89.7381
primes of bad reduction: 2, 3, 5, 383, 5147, 719745749
regulator: 1834637737.27132652046161263045812007459677686765926962705404
submitted by: jesper-petersen
submitted at: 2026-10-20 20:56:16 UTC
last updated: 2026-10-20 20:56:16 UTC

Witness: 11 independent points log in to add more points →

(-324124, 37677551)
(-315269, 64302954)
(-307690, 79629835)
(-295670, 98097885)
(-251336, 139978737)
(-249040, 141510415)
(-225224, 155068401)
(-201580, 165165935)
(-144710, 180112515)
(-105506, 185192997)
(-103025, 185411340)

Commentary

Historical rank-11 Mordell curve y^2 = x^3 + 35470887868736225, attributed to Noam Elkies (1999) in Tom Womack's Mordell curve table and his 2003.

last edited by jesper-petersen at 2026-10-20 20:56:17 UTC · history

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