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curve #1581

y² = x³ + x² − 3009x + 139231

a-invariants: [0, 1, 0, -3009, 139231]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 4405696 ☆ record for ℤ/2ℤ torsion, rank ≥ 4
discriminant (Δ): -6751359041536
Faltings height: 1.1503
naive height: 37.2253
primes of bad reduction: 2, 23, 41, 73
regulator: 12.66445480481246979325369448186401209380340478
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:22:00 UTC
last updated: 2026-09-25 01:22:00 UTC

Witness: 4 independent points log in to add more points →

(11, 328)
(93, 820)
(-30, 451)
(-21, 440)

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 01:22:00 UTC · history

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