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curve #1279

y² = x³ − x² − 53026080x + 143561892672

a-invariants: [0, -1, 0, -53026080, 143561892672]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 40027043760
discriminant (Δ): 640865692865981975040000
Faltings height: 3.3355
naive height: 64.9725
primes of bad reduction: 2, 3, 5, 11, 31, 41, 79, 151
regulator: 100.568021316465048195357597357622935352586278996
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:24:38 UTC
last updated: 2026-09-24 17:24:38 UTC

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

(314, 356290)
(13349, 1346950)
(195474, 86364450)
(114621/4, 37653375/8)
(834896/289, 591116680/4913)

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 2026-09-24 17:24:39 UTC · history

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