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curve #1407

y² + xy = x³ − 7159242129940010x + 233157123445386075102372

a-invariants: [1, 0, 0, -7159242129940010, 233157123445386075102372]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 3769747410
discriminant (Δ): 1861574246074146370176957616484253696000
Faltings height: 7.4633
naive height: 121.1351
primes of bad reduction: 2, 3, 5, 11, 13, 29, 157, 193
regulator: 67.0856676827923225891482941830067478661322
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:22:34 UTC
last updated: 2026-09-24 23:22:34 UTC

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

(10483350388/289, 715092314326694/4913)
(46946158132/961, -604305634310/29791)

Commentary

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:22:35 UTC · history

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