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curve #1519

y² + xy = x³ − 107717x + 14239681

a-invariants: [1, 0, 0, -107717, 14239681]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 282286
discriminant (Δ): -7716972324192256
Faltings height: 1.8060
naive height: 46.4675
primes of bad reduction: 2, 29, 31, 157
regulator: 3.0367214056053739476547517843404098179686602
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:48:50 UTC
last updated: 2026-09-25 00:48:50 UTC

Witness: 3 independent points log in to add more points →

(1970, 85319)
(-350, 3191)
(-270, 4999)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 00:48:50 UTC · history

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