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curve #1567

y² + xy = x³ − 181665167180x + 37065322475812752

a-invariants: [1, 0, 0, -181665167180, 37065322475812752]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 2615851410
discriminant (Δ): -209795762244854805061067328094560000
Faltings height: 5.4907
naive height: 89.8261
primes of bad reduction: 2, 3, 5, 19, 23, 61, 3271
regulator: 121.32225006217315230008862965360590940337079
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:11:19 UTC
last updated: 2026-09-25 01:11:19 UTC

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

(687334, 486397168)
(86264056/289, 476475370244/4913)
(8642116/25, 15578411096/125)

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 01:11:19 UTC · history

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