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curve #1314

y² + xy = x³ − x² − 663080916x + 6572685336996

a-invariants: [1, -1, 0, -663080916, 6572685336996]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 13095819956898
discriminant (Δ): -2920067751842641348104996
Faltings height: 3.7339
naive height: 72.5510
primes of bad reduction: 2, 3, 7, 19, 43, 127, 379, 881
regulator: 17231.032316116977881795312184102780598498603788274
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:36 UTC
last updated: 2026-09-24 17:30:36 UTC

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

(16720, 391614)
(-1781, 2784410)
(133741/9, 413005/27)
(371254/25, 1942032/125)
(595/4, 20354737/8)
(304351/25, 68213934/125)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:30:36 UTC · history

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