curve #4691

y² = x³ + 68513487607153

a-invariants: [0, 0, 0, 0, 68513487607153]
c-invariants: [0, -59195653292580192]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 168987527427438277691643554724
discriminant (Δ): -2027850329129259332299722656688
Faltings height: 4.4943
naive height: 77.2392
primes of bad reduction: 2, 3, 11777, 5817567089
regulator: 244393257.3912712974330121970817194132491855499160970174348
submitted by: jesper-petersen
submitted at: 2026-10-20 20:44:59 UTC
last updated: 2026-10-20 20:44:59 UTC

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

(-40053, 2063674)
(-38353, 3478224)
(-36754, 4343283)
(-36049, 4654752)
(-35748, 4778119)
(-35284, 4958457)
(-15154, 8064333)
(-7294, 8253813)
(4838, 8284125)
(9336, 8326297)

Commentary

Historical rank-10 Mordell curve y^2 = x^3 + 68513487607153, found by Noam Elkies (2001), as documented in Tom Womack's Mordell curve table and his 2003 thesis.

last edited by jesper-petersen at 2026-10-20 20:44:59 UTC · history