curve #4706

y² = x³ + 66265

a-invariants: [0, 0, 0, 0, 66265]
c-invariants: [0, -57252960]
rank (lower bound): ≥ 5
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 474233424300
discriminant (Δ): -1896933697200
Faltings height: 1.0348
naive height: 35.7260
primes of bad reduction: 2, 3, 5, 29, 457
regulator: 544.467074224691407356802740401556264557340956314
submitted by: jesper-petersen
submitted at: 2026-10-20 21:08:46 UTC
last updated: 2026-10-20 21:08:46 UTC

Witness: 5 independent points log in to add more points →

(-24, 229)
(-9, 256)
(-6, 257)
(24, 283)
(51, 446)

Commentary

Historical rank-5 Mordell curve y^2 = x^3 + 66265, documented by Gebel, Pethő and Zimmer (1998), "On Mordell's Equation", and in Tom Womack's Mordell curve table.

last edited by jesper-petersen at 2026-10-20 21:08:46 UTC · history