curve #2709

y² + xy = x³ − 32174355462579650355x + 416162791151353397699582660577

a-invariants: [1, 0, 0, -32174355462579650355, 416162791151353397699582660577]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 184371560352210
discriminant (Δ): -72687095701612332271410771374105466234756967352238981000000000
Faltings height: 10.5511
naive height: 149.9249
primes of bad reduction: 2, 3, 5, 7, 11, 47, 4519, 375787
regulator: 3023.0688774409439905047301690238696815912196
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:43 UTC
last updated: 2026-09-26 20:18:43 UTC

van Beek (2015). Source: https://dujella.github.io/tors/z9old3.html (curve entry 11). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:18:43 UTC · history