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curve #1239

y² + xy = x³ − 2906160x + 1905709311

a-invariants: [1, 0, 0, -2906160, 1905709311]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 542770695987
discriminant (Δ): 1558582879418246097
Faltings height: 2.4368
naive height: 56.2606
primes of bad reduction: 3, 13, 101, 157, 181, 373
regulator: 521.22415832693829829171882554949012880549882020830
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:37:51 UTC
last updated: 2026-09-24 14:37:51 UTC

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

(-1725, 43131)
(93, 40404)
(651, 16698)
(1353, 20559)
(1911, 56766)
(4941, 326436)

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 14:37:51 UTC · history

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