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curve #780

y² = x³ − 70554967x + 233196593050

a-invariants: [0, 0, 0, -70554967, 233196593050]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 31693061874096605785624
discriminant (Δ): -1014177979971091385139968
Faltings height: 3.3893
naive height: 65.8734
primes of bad reduction: 2, 830233, 4771711958284091
regulator: 5564810.74487482760735843981637031316596789197058587934220431
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:38:51 UTC
last updated: 2026-09-18 12:38:51 UTC

Witness: 11 independent points log in to add more points →

(4937, -72118)
(4949, 72346)
(4366, -91532)
(5127, 78932)
(6923, 276676)
(2553, -264026)
(3073, 213074)
(17867, -2162468)
(22225/4, 901825/8)
(5419, 99956)
(4621, -76402)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:38:52 UTC · history

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