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curve #1271

y² = x³ + x² − 9188960x + 10717630900

a-invariants: [0, 1, 0, -9188960, 10717630900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1565566960
discriminant (Δ): 5667051806343680000
Faltings height: 2.6546
naive height: 59.7141
primes of bad reduction: 2, 5, 31, 41, 89, 173
regulator: 33.4956590633896718841963549053004275645421768681
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:16:27 UTC
last updated: 2026-09-24 17:16:27 UTC

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

(3010, 101680)
(-1910, 145960)
(-270, 114800)
(128770/9, 45247600/27)
(26570, 4304040)

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 17:16:27 UTC · history

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