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curve #1284

y² = x³ − x² − 659312033x + 6464915195937

a-invariants: [0, -1, 0, -659312033, 6464915195937]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 84852484800
discriminant (Δ): 287997767069369241600000000
Faltings height: 3.8994
naive height: 72.5337
primes of bad reduction: 2, 3, 5, 37, 41, 43, 271
regulator: 339.378433108586693597770647583077096858234667336
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:25:29 UTC
last updated: 2026-09-24 17:25:29 UTC

Witness: 5 independent points log in to add more points →

(20512, 1253375)
(-9569, 3449288)
(18921, 873792)
(-11863, 3552000)
(-5352407/289, 17246440000/4913)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:25:30 UTC · history

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