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curve #1268

y² + xy + y = x³ + x² − 272288x + 30461906

a-invariants: [1, 1, 1, -272288, 30461906]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1049432925
discriminant (Δ): 888152793608109375
Faltings height: 2.1423
naive height: 49.1575
primes of bad reduction: 3, 5, 31, 41, 101, 109
regulator: 39.6835481985993633189419411268445159825615151781
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:15:54 UTC
last updated: 2026-09-24 17:15:54 UTC

Witness: 5 independent points log in to add more points →

(60, 3757)
(464, -2303)
(4605, 308272)
(565, -7858)
(-520, 5897)

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 17:15:54 UTC · history

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