curve #2119

y² + xy = x³ − 333848836163677156595x + 23118493712440422090809079478881

a-invariants: [1, 0, 0, -333848836163677156595, 23118493712440422090809079478881]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/10ℤ
conductor (N): 96439541661606
discriminant (Δ): -228507387882028771723106382409730412061916697717699303743385320448
Faltings height: 11.2211
naive height: 157.9595
primes of bad reduction: 2, 3, 11, 13, 31, 41, 43, 271, 7589
regulator: 2178.8695649252913568090534905874641142633198
submitted by: Steps Unbounded
submitted at: 2026-09-26 08:51:56 UTC
last updated: 2026-09-26 08:51:56 UTC

(7314361646176/289, 27301816244143729535/4913)
(28478480584450/2209, 475291182957696385007/103823)
(13693435267862145094/641659561, 82419936980414853145273031435/16253878339691)

Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=82/121 (t=s^2(2s-1)/(s-1)^2); conductor 96439541661606.

last edited by Steps Unbounded at 2026-09-26 08:54:18 UTC · history