curve #5686

y² = x³ + 26571003403624

a-invariants: [0, 0, 0, 0, 26571003403624]
c-invariants: [0, -22957346940731136]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 19062491990635751201721001152
discriminant (Δ): -304999871850172019227536018432
Faltings height: 4.3364
naive height: 75.3448
primes of bad reduction: 2, 3, 83, 40016571391
regulator: 463625510.2764452567310661745158539342724818976165624606798
submitted by: jesper-petersen
submitted at: 2026-10-24 09:05:36 UTC
last updated: 2026-10-24 09:05:36 UTC

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

(-29802, 319504)
(-23082, 3778016)
(-17382, 4617284)
(-762, 5154664)
(14625, 5449693)
(79770, 23112068)
(98310, 31252568)
(354438, 211076536)
(-37983/4, 40567793/8)
(221937/4, 112393417/8)

Commentary

Mordell curve obtained from the rational Burkhardt-quartic parametrization (u,v,w) = (3/4,5/4,-3/4), specialized at t = -125/52. PARI/GP 2.17.4 returned matching rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 09:05:36 UTC · history