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curve #766

y² + xy = x³ − x² − 14569x + 719329

a-invariants: [1, -1, 0, -14569, 719329]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 898281620938
discriminant (Δ): -23355322144388
Faltings height: 1.3165
naive height: 40.4851
primes of bad reduction: 2, 13, 3271, 10562303
regulator: 436.4134428997435185518489559298829273890636656210667
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:21:15 UTC
last updated: 2026-09-18 12:21:15 UTC

Witness: 7 independent points log in to add more points →

(67, 168)
(-24, 1039)
(-102, -1015)
(80, 207)
(119, 753)
(106, 545)
(41, -456)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:21:16 UTC · history

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