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curve #3452

y² = x³ − x² − 4021369x + 2911294969

a-invariants: [0, -1, 0, -4021369, 2911294969]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 22447563072
discriminant (Δ): 503893087871418077184
Faltings height: 2.7200
naive height: 57.2350
primes of bad reduction: 2, 3, 11, 19, 73, 79, 97
regulator: 160.664387578413539664983363484192298486395501446
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:37:21 UTC
last updated: 2026-09-27 05:37:21 UTC

Witness: 5 independent points log in to add more points →

(4389, 264176)
(-1463, 75240)
(1463, 12540)
(-1615, 72048)
(2651, 104280)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:37:21 UTC · history

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