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curve #1349

y² = x³ + x² − 2674433225x + 53223177298039

a-invariants: [0, 1, 0, -2674433225, 53223177298039]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 43121536946337856
discriminant (Δ): 494237869660419735185887232
Faltings height: 4.1127
naive height: 76.7346
primes of bad reduction: 2, 23, 41, 73, 359, 449, 1481
regulator: 33029.1048742026573009818023985947082977475069520810435
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:38 UTC
last updated: 2026-09-24 17:36:38 UTC

Witness: 8 independent points log in to add more points →

(-2825, 7794608)
(29485, 40208)
(8514, 5574073)
(-13175, 9282892)
(31639, 528448)
(28891, 268304)
(44922, 4871989)
(31146, 374371)

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 17:36:38 UTC · history

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