curve #4668

y² = x³ − 44865147851

a-invariants: [0, 0, 0, 0, -44865147851]
c-invariants: [0, 38763487743264]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 72463733700915237055236
discriminant (Δ): -869564804410982844662832
Faltings height: 3.2724
naive height: 62.5770
primes of bad reduction: 2, 3, 1433, 31308547
regulator: 21006193.311662162893888854830655916075318577684953386611
submitted by: David Renshaw
submitted at: 2026-10-20 19:26:47 UTC
last updated: 2026-10-20 19:26:47 UTC

Witness: 9 independent points log in to add more points →

(3651, 61660)
(3695, 74718)
(4623, 232246)
(5315, 324468)
(10563, 1064764)
(57155, 13662468)
(28337/4, 4459017/8)
(36785/4, 6848631/8)
(67193/16, 10936269/64)

Commentary

Mordell curve y^2 = x^3 - 44865147851, rank exactly 9 (PARI ellrank 2-descent: lower = upper = 9). Found by a Mestre-Nagao sieve over all |k| <= 10^12 (a_p via sextic residue classes for p = 1 mod 3), top candidates certified with ellrank.

last edited by David Renshaw at 2026-10-20 19:26:47 UTC · history