curve #5728

y² + y = x³ − 1119017686156

a-invariants: [0, 0, 1, 0, -1119017686156]
c-invariants: [0, 966831280838568]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 247348263097159230659409
discriminant (Δ): -540950651393487237452127483
Faltings height: 3.8085
naive height: 69.0101
primes of bad reduction: 3, 281, 589965829
regulator: 29107070.544833611644608191488271679992828837576735420125
submitted by: jesper-petersen
submitted at: 2026-10-24 17:00:14 UTC
last updated: 2026-10-24 17:00:14 UTC

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

(10446, 144355)
(10608, 273307)
(11212, 538916)
(11356, 587739)
(52449/4, 8524355/8)
(17736, 2111899)
(26052, 4069723)
(36196, 6804644)
(395412, 248639908)

Commentary

Constructed by specializing a rank-four Mordell family obtained from a rational parametrization of the Burkhardt quartic. The construction parameters are (u,v,w) = (-5,4,-2), with specialization t = -141/74. An archived PARI/GP 2.17.4 computation returned matching rank bounds [9,9] together with nine rational points.

last edited by jesper-petersen at 2026-10-24 17:00:15 UTC · history