curve #5743

y² + y = x³ − 438610968495253

a-invariants: [0, 0, 1, 0, -438610968495253]
c-invariants: [0, 378959876779898376]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 83107979287636435376946891717267
discriminant (Δ): -83107979287636435376946891717267
Faltings height: 4.8037
naive height: 80.9524
primes of bad reduction: 3, 23, 4423, 5748750353
regulator: 16039380571.1872491504289847640711801203136168288200529857119
submitted by: jesper-petersen
submitted at: 2026-10-24 18:12:35 UTC
last updated: 2026-10-24 18:12:35 UTC

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

(83407, 11900790)
(93547, 19494170)
(134395, 44596341)
(135985, 45563283)
(150169, 54293732)
(219055, 100363158)
(439237, 290349800)
(1203775/9, 1193571082/27)
(5803441/64, 8971077609/512)
(2081329/25, 1470671892/125)
(6409285/49, 14549379713/343)

Commentary

Constructed from the Burkhardt quartic via the rational Bruin–Nasserden parametrization with parameters (u,v,w)=(9/6,-12/6,-10/6) and specialization t=-421/568. The specialization was selected through a three-stage Mestre–Nagao sieve over 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [11,11] for this model and its rationally 3-isogenous partner.

last edited by jesper-petersen at 2026-10-24 18:12:35 UTC · history