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curve #1267

y² + xy + y = x³ + x² − 237413x + 44411906

a-invariants: [1, 1, 1, -237413, 44411906]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1049432925
discriminant (Δ): 548984598890625
Faltings height: 1.7957
naive height: 48.7463
primes of bad reduction: 3, 5, 31, 41, 101, 109
regulator: 79.3670963971987266378838822536890319651230303560
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:15:43 UTC
last updated: 2026-09-24 17:15:43 UTC

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

(440, 4817)
(2535/4, 95111/8)
(-490, 6832)
(6, 6553)
(-335, 9467)

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 17:15:43 UTC · history

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