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curve #4685

y² = x³ − 463066403167

a-invariants: [0, 0, 0, 0, -463066403167]
c-invariants: [0, 400089372336288]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 7719497774712813154676004
discriminant (Δ): -92633973296553757856112048
Faltings height: 3.6614
naive height: 67.2454
primes of bad reduction: 2, 3, 269, 1721436443
regulator: 17548332.911807617981078332696723236695746955018609371830
submitted by: jesper-petersen
submitted at: 2026-10-20 20:38:19 UTC
last updated: 2026-10-20 20:38:19 UTC

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

(8326, 337803)
(8632, 424401)
(10706, 874093)
(12322, 1186509)
(12916, 1300623)
(23966, 3647227)
(24742, 3831861)
(36662, 6986731)
(237751/25, 78762876/125)

Commentary

Historical rank-9 Mordell curve y^2 = x^3 - 463066403167, found by Tom Womack (2000) and documented in his 2003 thesis.

last edited by jesper-petersen at 2026-10-20 20:38:19 UTC · history

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