curve #5732

y² + y = x³ + 24022926973844713

a-invariants: [0, 0, 1, 0, 24022926973844713]
c-invariants: [0, -20755808905401832248]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 34611639706896014723792957766081
discriminant (Δ): -249307640808771994055480674789081443
Faltings height: 5.4709
naive height: 88.9587
primes of bad reduction: 3, 7, 5189, 9949, 5426611
regulator: 70665850510.1803895268562304901860487747198614532278386841072
submitted by: jesper-petersen
submitted at: 2026-10-24 17:23:00 UTC
last updated: 2026-10-24 17:23:00 UTC

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

(458969, 347427566)
(2269681/4, 3637254413/8)
(10441739, 33741457011)
(-18468667/121, 190416837439/1331)
(-5904503/196, 425059575473/2744)
(-4008991/16, 5827981617/64)
(1812307/9, 4844084788/27)
(10194289/16, 34026818647/64)
(18095329/100, 173055130483/1000)
(30916193/16, 172187208945/64)
(193135159/25, 2684128638923/125)

Commentary

Constructed from the Burkhardt quartic using the rational Bruin–Nasserden parametrization with parameters (u,v,w)=(-18/5,1/5,-10/5) and specialization t=-2182/1387. The specialization was selected by a three-stage Mestre–Nagao sieve using 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [11,11].

last edited by jesper-petersen at 2026-10-24 17:23:00 UTC · history