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curve #4679

y² = x³ + 1632201497

a-invariants: [0, 0, 0, 0, 1632201497]
c-invariants: [0, -1410222093408]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 95906942165125476324
discriminant (Δ): -1150883305981505715888
Faltings height: 2.7201
naive height: 55.9495
primes of bad reduction: 2, 3, 10891, 149867
regulator: 327165.730742306611160026782356550721003893302803577390
submitted by: jesper-petersen
submitted at: 2026-10-20 20:31:26 UTC
last updated: 2026-10-20 20:31:26 UTC

Witness: 8 independent points log in to add more points →

(-1177, 1292)
(-1088, 18555)
(-982, 26177)
(-656, 36741)
(-557, 38202)
(2708, 146597)
(2948, 165083)
(3538, 214287)

Commentary

Historical Mordell curve of rank 8, attributed to Noam Elkies (1999) in Tom Womack's Mordell curve table.

last edited by jesper-petersen at 2026-10-20 20:31:27 UTC · history

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