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curve #1304

y² = x³ − x² − 31736142881x + 874617713691681

a-invariants: [0, -1, 0, -31736142881, 874617713691681]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 10956498893760
discriminant (Δ): 1715249092059282700263511203840000
Faltings height: 5.0706
naive height: 84.1558
primes of bad reduction: 2, 3, 5, 7, 23, 137, 193, 383
regulator: 3890.1832676398796398085377237541335079111601784867
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:28:54 UTC
last updated: 2026-09-24 17:28:54 UTC

Witness: 6 independent points log in to add more points →

(-5504, 32390225)
(-2604275/36, 11413019681/216)
(179583, 31094616)
(9121, 24205600)
(-33775, 43680384)
(-8017, 33593616)

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 17:28:54 UTC · history

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