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curve #1585

y² + xy = x³ + x² − 1131x + 14121

a-invariants: [1, 1, 0, -1131, 14121]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 6399618
discriminant (Δ): 729556452
Faltings height: 0.5518
naive height: 32.7076
primes of bad reduction: 2, 3, 19, 73, 769
regulator: 10.11562630605171395069759579567351842903853690
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:22:40 UTC
last updated: 2026-09-25 01:22:40 UTC

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

(24, 27)
(56, 333)
(-20, 181)
(-39, 48)

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 01:22:40 UTC · history

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