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curve #4684

y² = x³ + 185418133372

a-invariants: [0, 0, 0, 0, 185418133372]
c-invariants: [0, -160201267233408]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 309418957648411020813456
discriminant (Δ): -14852109967123728999045888
Faltings height: 3.5089
naive height: 65.4149
primes of bad reduction: 2, 3, 11467, 4042429
regulator: 8883374.6020706143014254573394148119107528059726888478718
submitted by: jesper-petersen
submitted at: 2026-10-20 20:37:13 UTC
last updated: 2026-10-20 20:37:13 UTC

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

(-3238, 389190)
(258, 430622)
(2762, 454410)
(3629, 482919)
(5037, 559655)
(8354, 876606)
(9533, 1025553)
(12162, 1408670)
(128234, 45922326)

Commentary

Historical rank-9 Mordell curve y^2 = x^3 + 185418133372, found by Tom Womack (2000) and documented in his 2003 thesis.

last edited by jesper-petersen at 2026-10-20 20:37:13 UTC · history

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