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curve #1330

y² = x³ + x² − 4932661560x + 129720255016564

a-invariants: [0, 1, 0, -4932661560, 129720255016564]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 48324055603376
discriminant (Δ): 411511901229326906098910554112
Faltings height: 4.4579
naive height: 78.5710
primes of bad reduction: 2, 7, 29, 37, 71, 109, 223, 233
regulator: 917.1874590035688539494380482725173489168732285883699
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:33:20 UTC
last updated: 2026-09-24 17:33:20 UTC

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

(-75868, 8201494)
(-20701, 14931868)
(2056186/81, 3329806564/729)
(20914, 5975508)
(72650, 12442508)
(31876, 2208234)
(145794, 50095612)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:33:20 UTC · history

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