curve #1454

y² + xy = x³ − x² − 8817609605361133895505x + 318694379140227532111456792235625

a-invariants: [1, -1, 0, -8817609605361133895505, 318694379140227532111456792235625]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 335169366127470
discriminant (Δ): 2005444069636092172283491043681002402211063705972992679840100
Faltings height: 11.0852
naive height: 163.2067
primes of bad reduction: 2, 3, 5, 7, 31, 71, 457, 599, 883
regulator: 623.539822612484116470186817672192739649519
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:58:19 UTC
last updated: 2026-09-24 23:58:19 UTC

(38175670982286436446/433930561, 135249058278611136000835925319/9039207516191)
(-786731528219023574840/9453089529, -20054209010274277692545465782705/919095535636083)

Torsion Z/6+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:58:19 UTC · history