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curve #1273

y² = x³ + x² − 517680x + 160352164

a-invariants: [0, 1, 0, -517680, 160352164]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 585882128
discriminant (Δ): -2252838045699324928
Faltings height: 2.2517
naive height: 51.3111
primes of bad reduction: 2, 13, 23, 29, 41, 103
regulator: 17.8801907165853575051349562978611321600864536243
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:17:20 UTC
last updated: 2026-09-24 17:17:20 UTC

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

(-166, 15548)
(3422, 196144)
(1429/4, 36777/8)
(6280/9, 318734/27)
(432, 4186)

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 17:17:20 UTC · history

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