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curve #1495

y² + xy + y = x³ − 231x − 442

a-invariants: [1, 0, 1, -231, -442]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 59450 ☆ record for ℤ/2ℤ torsion, rank ≥ 3
discriminant (Δ): 706860500
Faltings height: 0.3899
naive height: 27.9346
primes of bad reduction: 2, 5, 29, 41
regulator: 1.2628467231688845352482154290022966768235041
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:39:19 UTC
last updated: 2026-09-25 00:39:19 UTC

Witness: 3 independent points log in to add more points →

(-7, 32)
(22, 61)
(17, 16)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:39:19 UTC · history

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