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curve #1564

y² + xy = x³ − 8170675396524x + 18949896093734770320

a-invariants: [1, 0, 0, -8170675396524, 18949896093734770320]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 1242248154
discriminant (Δ): -120220268629393950963858259616436437184768
Faltings height: 6.5719
naive height: 102.2998
primes of bad reduction: 2, 3, 7, 73, 97, 4177
regulator: 545.09869610623302272634672325423231107851930
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:08:19 UTC
last updated: 2026-09-25 01:08:19 UTC

Witness: 3 independent points log in to add more points →

(-732252439/256, 17821556946083/4096)
(904389016320/162409, 791010233855195580/65450827)
(536048016, 12410520962556)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:08:19 UTC · history

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