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curve #1555

y² + xy = x³ − 66174826178306x + 218815508200934921412

a-invariants: [1, 0, 0, -66174826178306, 218815508200934921412]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/7ℤ
conductor (N): 3463956678
discriminant (Δ): -2137911071088046646554459322745210424786944
Faltings height: 6.8744
naive height: 107.1927
primes of bad reduction: 2, 3, 7, 13, 29, 31, 7057
regulator: 46.840739502150783346612107767684649645222255
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:54:52 UTC
last updated: 2026-09-25 00:54:52 UTC

Witness: 3 independent points log in to add more points →

(3301006, 6026772898)
(5185252, 3882944302)
(1740098116/361, 23578611215482/6859)

Commentary

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:54:52 UTC · history

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