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curve #1211

y² = x³ + x² − 445020x + 71792644

a-invariants: [0, 1, 0, -445020, 71792644]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 44968690156 ☆ record for ℤ/2ℤ torsion, rank ≥ 6
discriminant (Δ): 3404706883041281792
Faltings height: 2.2574
naive height: 50.6312
primes of bad reduction: 2, 13, 17, 43, 53, 101
regulator: 225.35585877746084606680698345878389637596018570133
submitted by: Michael Rubinstein
submitted at: 2026-09-24 13:35:32 UTC
last updated: 2026-09-24 13:35:32 UTC

Witness: 6 independent points log in to add more points →

(164, 1802)
(-48, 9646)
(-516, 12818)
(588, 3710)
(5080/9, 23426/27)
(-636, 9898)

Commentary

Torsion 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 13:35:32 UTC · history

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