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curve #1233

y² = x³ + x² − 422415x + 88452529

a-invariants: [0, 1, 0, -422415, 88452529]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 1188797217664
discriminant (Δ): 1433235323965636352
Faltings height: 2.2042
naive height: 50.4748
primes of bad reduction: 2, 7, 31, 71, 617, 977
regulator: 2163.1830614475910351579321226325982782688314268250
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:36:50 UTC
last updated: 2026-09-24 14:36:50 UTC

Witness: 6 independent points log in to add more points →

(-120, 11723)
(497, 1234)
(4816, 331329)
(-1697/9, 343052/27)
(2605/4, 75891/8)
(18441/16, 2155181/64)

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 14:36:51 UTC · history

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