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curve #1582

y² = x³ + x² − 15249x + 716431

a-invariants: [0, 1, 0, -15249, 716431]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 4594624
discriminant (Δ): 2059567775744
Faltings height: 1.2078
naive height: 40.5105
primes of bad reduction: 2, 17, 41, 103
regulator: 10.41641310513578030289719141633201079425364568
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:22:10 UTC
last updated: 2026-09-25 01:22:10 UTC

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

(170, 1751)
(-221/9, 28016/27)
(-139, 412)
(891, 26368)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:22:10 UTC · history

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