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curve #1323

y² + xy + y = x³ − 1052379025x + 13115318303120

a-invariants: [1, 0, 1, -1052379025, 13115318303120]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 7566702958578
discriminant (Δ): 282739960537786982578380804
Faltings height: 3.9587
naive height: 73.9366
primes of bad reduction: 2, 3, 17, 43, 73, 523, 619
regulator: 748.92565617475082833041008944475158036439483648979
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:32:08 UTC
last updated: 2026-09-24 17:32:08 UTC

Witness: 6 independent points log in to add more points →

(2023, 3314804)
(106513, 33254672)
(17818, 135959)
(1984801/25, 2587038934/125)
(-37451, 38462)
(61234, 13321463)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:32:08 UTC · history

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