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curve #1411

y² = x³ + x² − 65x − 161

a-invariants: [0, 1, 0, -65, -161]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 1088 ☆ record for ℤ/2ℤ torsion, rank ≥ 2
discriminant (Δ): 9469952
Faltings height: 0.0434
naive height: 24.1521
primes of bad reduction: 2, 17
regulator: 0.531665631644888496256262446826464461629107
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:24:37 UTC
last updated: 2026-09-24 23:24:37 UTC

Witness: 2 independent points log in to add more points →

(-5, 8)
(11, 24)

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 23:24:38 UTC · history

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