curve #2691

y² + xy = x³ − 1461055764835991591052x + 27792751576411398242819550412944

a-invariants: [1, 0, 0, -1461055764835991591052, 27792751576411398242819550412944]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 1192831413867834
discriminant (Δ): -134083694914877524631235431053014505424287198533133512496568572416
Faltings height: 11.2061
naive height: 158.3278
primes of bad reduction: 2, 3, 13, 19, 23, 31, 47, 127, 379, 499
regulator: 4133.1175508327053162002128063084464621367941
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:17:56 UTC
last updated: 2026-09-26 20:17:56 UTC

Voznyy (2021). Source: https://dujella.github.io/tors/z9old3.html (curve entry 16). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:17:56 UTC · history