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curve #3442

y² = x³ − x² − 559889409x + 313921714689

a-invariants: [0, -1, 0, -559889409, 313921714689]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4407664742592
discriminant (Δ): 11190244886259034532473995264
Faltings height: 4.0716
naive height: 72.0434
primes of bad reduction: 2, 3, 23, 31, 41, 577, 1361
regulator: 3720.8745617389378629812471423304665814135785035376
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:34:19 UTC
last updated: 2026-09-27 05:34:19 UTC

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

(-3165, 1433268)
(-5856, 1841679)
(-22255, 1323328)
(-2161, 1230344)
(44113, 7839360)
(295153689/11881, 1706192803584/1295029)

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 2026-09-27 05:34:19 UTC · history

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