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curve #1609

y² + xy = x³ + 688116585x + 1991583208225

a-invariants: [1, 0, 0, 688116585, 1991583208225]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 2680891070
discriminant (Δ): -22566268002590249075678683000
Faltings height: 4.1296
naive height: 72.6620
primes of bad reduction: 2, 5, 11, 13, 19, 79, 1249
regulator: 226.7475657616525416085098649072656554515774357
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:31:58 UTC
last updated: 2026-09-25 01:31:58 UTC

Witness: 4 independent points log in to add more points →

(54040, 14008375)
(166900, 68952385)
(-2548, 472147)
(12392, 3518247)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:31:58 UTC · history

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