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curve #1405

y² + xy = x³ + 1102681704055360x − 7651093618760970652608

a-invariants: [1, 0, 0, 1102681704055360, -7651093618760970652608]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 2622052290
discriminant (Δ): -111097483079635666647906513477894305015625000000
Faltings height: 7.7154
naive height: 115.5232
primes of bad reduction: 2, 3, 5, 11, 13, 17, 157, 229
regulator: 203.622990810958595993923703590640776117836
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:22:14 UTC
last updated: 2026-09-24 23:22:14 UTC

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

(132634483654/7921, 87784318345420172/704969)
(44783134728826/11449, 299698027589682085934/1225043)

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 23:22:14 UTC · history

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