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curve #1469

y² + xy = x³ − 1195742680x + 15666350994752

a-invariants: [1, 0, 0, -1195742680, 15666350994752]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/8ℤ
conductor (N): 2607990
discriminant (Δ): 3390031298656577628900000000
Faltings height: 4.0782
naive height: 74.3197
primes of bad reduction: 2, 3, 5, 7, 11, 1129
regulator: 4.15846994338320060458326699704362080844498
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:13:18 UTC
last updated: 2026-09-25 00:13:18 UTC

Witness: 2 independent points log in to add more points →

(-1846, 4227908)
(32174, 3224318)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:13:19 UTC · history

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