curve #2695

y² + xy = x³ − 1120394540235646336605x + 20279431254320501002290372230577

a-invariants: [1, 0, 0, -1120394540235646336605, 20279431254320501002290372230577]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 176365492125690
discriminant (Δ): -87651854983446432648203471363271989461442981596576679424000000000
Faltings height: 11.1645
naive height: 157.6975
primes of bad reduction: 2, 3, 5, 7, 23, 47, 907, 856567
regulator: 827.29663232568685363172000136984722085590518
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:07 UTC
last updated: 2026-09-26 20:18:07 UTC

Eroshkin (2009). Source: https://dujella.github.io/tors/z9old3.html (curve entry 7). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:18:07 UTC · history