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curve #1474

y² + xy = x³ − 746486487925122x + 7850205699850732736196

a-invariants: [1, 0, 0, -746486487925122, 7850205699850732736196]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 1175922426
discriminant (Δ): -12399425074260011048604176917689532416
Faltings height: 6.9278
naive height: 114.3528
primes of bad reduction: 2, 3, 7, 19, 23, 79, 811
regulator: 134.270485801554950681955762548950212037859
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:18:19 UTC
last updated: 2026-09-25 00:18:19 UTC

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

(30539185341/1936, -550820446449/85184)
(41911424205/2704, 263674814453673/140608)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:18:19 UTC · history

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