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curve #1716

y² = x³ − 757332687x + 8012667222866

a-invariants: [0, 0, 0, -757332687, 8012667222866]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 77723228520
discriminant (Δ): 64072901497869152249760000
Faltings height: 3.8578
naive height: 72.9495
primes of bad reduction: 2, 3, 5, 7, 31, 83, 11987
regulator: 131.976965463288576791829531206420181357153612284
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:14:58 UTC
last updated: 2026-09-25 06:14:58 UTC

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

(-2893, 3190520)
(-6458, 3554460)
(12421, 722610)
(61897, 14081130)
(15277, 91350)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:14:58 UTC · history

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