curve #5751

y² + y = x³ − 42064778996666

a-invariants: [0, 0, 1, 0, -42064778996666]
c-invariants: [0, 36343969053119208]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1507693319606626100946419409
discriminant (Δ): -764400513040559433179834640363
Faltings height: 4.4130
naive height: 76.2636
primes of bad reduction: 3, 13, 17, 58565651231
regulator: 1669883813.854683607130395813930258074055705721474990308810
submitted by: jesper-petersen
submitted at: 2026-10-24 18:44:22 UTC
last updated: 2026-10-24 18:44:22 UTC

Witness: 10 independent points log in to add more points →

(45032, 7018173)
(47632, 8124226)
(333593/4, 185557303/8)
(100126, 31011610)
(173732, 72122498)
(176696, 73990845)
(2761057/36, 4368771611/216)
(1480726/25, 1609131026/125)
(3306056/25, 5956336954/125)
(2320665334/37249, 101606589283333/7189057)

Commentary

Constructed using the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(6/8,7/8,-5/8) and specialization t=-641/625. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 18:44:23 UTC · history