curve #5414

y² + y = x³ + 7298938824452822

a-invariants: [0, 0, 1, 0, 7298938824452822]
c-invariants: [0, -6306283144327238424]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 260909742090503810360561327163
discriminant (Δ): -23014587440061250608094754107721067
Faltings height: 5.2723
naive height: 86.5762
primes of bad reduction: 3, 11, 2978854739089
regulator: 5894474984.095893739746354032420659301662395691811724178677
submitted by: jesper-petersen
submitted at: 2026-10-21 22:19:44 UTC
last updated: 2026-10-21 22:19:44 UTC

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

(95832, 90438034)
(334350, 211366741)
(701644, 593903442)
(3595801/4, 6852741441/8)
(-62454887/324, 68123441825/5832)
(-1662782/9, 850643038/27)
(-6137087/64, 41014957695/512)
(-262863/16, 5466103735/64)
(-20042/9, 2306711575/27)
(2584846/9, 4753040174/27)

Commentary

Rank-10 elliptic curve with j-invariant 0, found using Mestre's polynomial cube-completion construction from the integer sextuple (-45,-13,-1,9,11,39).

last edited by jesper-petersen at 2026-10-21 22:19:44 UTC · history