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curve #1274

y² = x³ + x² − 8555320x + 9628692084

a-invariants: [0, 1, 0, -8555320, 9628692084]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 585882128
discriminant (Δ): 1221755506303035392
Faltings height: 2.5983
naive height: 59.4998
primes of bad reduction: 2, 13, 23, 29, 41, 103
regulator: 35.7603814331707150102699125957222643201729072481
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:18:21 UTC
last updated: 2026-09-24 17:18:21 UTC

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

(-686, 123188)
(1154, 35972)
(4052, 203734)
(190810/81, 36833212/729)
(1890, 14628)

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 17:18:21 UTC · history

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