curve #6008

y² + y = x³ + 88013558424

a-invariants: [0, 0, 1, 0, 88013558424]
c-invariants: [0, -76043714478552]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1115479651175837012590281
discriminant (Δ): -3346438953527511037770843
Faltings height: 3.3847
naive height: 63.9247
primes of bad reduction: 3, 449, 784085153
regulator: 13637786.043975132221779241867155046810024559015337252400
submitted by: jesper-petersen
submitted at: 2026-10-27 22:40:16 UTC
last updated: 2026-10-27 22:40:16 UTC

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

(-3564, 206744)
(-1668, 288743)
(-1408, 291928)
(-1074, 294575)
(4616, 431704)
(36569/4, 7384865/8)
(17162, 2267776)
(19812, 2804376)
(33668, 6184807)

Commentary

Constructed from the Burkhardt quartic using the rational Bruin–Nasserden parametrization with parameters (u,v,w)=(-1,2,2) and specialization t=-446/127. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-27 22:40:16 UTC · history