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curve #1325

y² = x³ + x² − 223282040x + 1265447468404

a-invariants: [0, 1, 0, -223282040, 1265447468404]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 22378025224048 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
discriminant (Δ): 20560878541068049041508352
Faltings height: 3.6555
naive height: 69.2854
primes of bad reduction: 2, 13, 17, 103, 127, 149, 191
regulator: 1244.437490939535603602473413214429472002295419971835
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:32:29 UTC
last updated: 2026-09-24 17:32:29 UTC

Witness: 7 independent points log in to add more points →

(20844, 2380742)
(23522, 3004716)
(-152510/9, 11563604/27)
(7636, 75946)
(10938, 363220)
(12810, 712348)
(28893/4, 1375283/8)

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 17:32:29 UTC · history

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