curve #1266

y² + xy = x³ − 8793921408287667177030x + 317410986657047325272998908855652

a-invariants: [1, 0, 0, -8793921408287667177030, 317410986657047325272998908855652]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 2258228975265200784470
discriminant (Δ): 5712961115599304789086078939345698283657473914335596019712000
Faltings height: 11.1067
naive height: 163.1986
primes of bad reduction: 2, 5, 13, 29, 37, 43, 73, 97, 163, 211, 277, 5581
regulator: 254197.5067650062035109693509969266301385060811133090
submitted by: hdeping
submitted at: 2026-09-24 16:49:01 UTC
last updated: 2026-09-24 16:49:01 UTC

(54122560184, -6168458714082)
(54166585542, 8973514714318)
(-674569717088/9, -636343754438636078/27)
(54127611404, -3299613263862)
(8781582245618732, -822922926795085121304470)
(268925393468, 131914307102637226)
(59763024572, 2304401901708970)

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=-808087/16936.

last edited by hdeping at 2026-09-27 08:24:56 UTC · history