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curve #1570

y² + xy = x³ − 62019632870195x + 187991400471206960562

a-invariants: [1, 0, 0, -62019632870195, 187991400471206960562]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 880838805
discriminant (Δ): 274556712288389653515745189039215234375
Faltings height: 6.5328
naive height: 106.8890
primes of bad reduction: 3, 5, 7, 11, 31, 73, 337
regulator: 105.26080808544308733140634418499684281477117
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:14:19 UTC
last updated: 2026-09-25 01:14:19 UTC

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

(1365892429/361, 18768485404537/6859)
(894761263/196, 141453226739/2744)
(6105808291/1369, 15925889854204/50653)

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 01:14:19 UTC · history

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