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curve #1699

y² + xy + y = x³ − x² − 4892351x + 3995885216

a-invariants: [1, -1, 1, -4892351, 3995885216]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 67158441
discriminant (Δ): 600763675407176297079
Faltings height: 2.7484
naive height: 57.8232
primes of bad reduction: 3, 7, 37, 47, 613
regulator: 53.65387648807715943334955879577438637062852880
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:12:08 UTC
last updated: 2026-09-25 06:12:08 UTC

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

(-2430, 40342)
(2364, 73900)
(21916, 3217495)
(-150303/64, 26346851/512)

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 06:12:08 UTC · history

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