curve #5735

y² + y = x³ − 279277554926

a-invariants: [0, 0, 1, 0, -279277554926]
c-invariants: [0, 241295807455848]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 33694251560051893094021643
discriminant (Δ): -33694251560051893094021643
Faltings height: 3.5772
naive height: 66.2341
primes of bad reduction: 3, 6427, 9533, 18233
regulator: 84892713.023096598890964010593073861358252449325964878601
submitted by: jesper-petersen
submitted at: 2026-10-24 17:42:13 UTC
last updated: 2026-10-24 17:42:13 UTC

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

(28289/4, 2182885/8)
(7682, 417206)
(9092, 687246)
(38369/4, 6213877/8)
(10862, 1001126)
(10886, 1005369)
(11336, 1085105)
(12206, 1240665)
(22718, 3383142)

Commentary

Constructed by specializing a rank-four Mordell family arising from a rational parametrization of the Burkhardt quartic. The construction parameters are (u,v,w) = (-2,1,4), with specialization t = 78/79.

last edited by jesper-petersen at 2026-10-24 17:42:13 UTC · history