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curve #4675

y² = x³ + 47550317

a-invariants: [0, 0, 0, 0, 47550317]
c-invariants: [0, -41083473888]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 244191525854452812
discriminant (Δ): -976766103417811248
Faltings height: 2.1308
naive height: 48.8777
primes of bad reduction: 2, 3, 317, 150001
regulator: 181126.7100150998977509028569546094248524574493214304
submitted by: jesper-petersen
submitted at: 2026-10-20 20:25:42 UTC
last updated: 2026-10-20 20:25:42 UTC

Witness: 7 independent points log in to add more points →

(-277, 5128)
(-121, 6766)
(-37, 6892)
(359, 9686)
(8327, 759890)
(-1399/4, 17467/8)
(2047/9, 207946/27)

Commentary

Historical Mordell curve y^2 = x^3 + 47550317, rank 7, listed by Tom Womack (2000) in his Mordell curve table.

last edited by jesper-petersen at 2026-10-20 20:25:42 UTC · history

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