curve #1216

y² + xy = x³ − 801598222309406030167646512525x + 1340218010187071010144873439749301626926500625

a-invariants: [1, 0, 0, -801598222309406030167646512525, 1340218010187071010144873439749301626926500625]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/6ℤ
conductor (N): 2133955072923930972049654590270 ☆ record for ℤ/6ℤ torsion, rank ≥ 9
discriminant (Δ): -742986841845104273640248969605835668577229339428654319790188862787640221867972757221376000000 ☆ record for ℤ/6ℤ torsion, rank ≥ 9
Faltings height: 16.5019 ☆ record for ℤ/6ℤ torsion, rank ≥ 9
naive height: 221.3415 ☆ record for ℤ/6ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 37, 41, 43, 47, 127, 719, 4733, 7253, 18911
regulator: 61991726.017993080851688028865057068792706945030580569395
submitted by: dujella
submitted at: 2026-09-24 14:16:45 UTC
last updated: 2026-09-24 14:16:45 UTC

(790071801566192, 34642044937854378014327)
(-726457590523390, -39232179492604220813185)
(-1339807100575790, -3023236219045337181425)
(625652233410050, 32918110979399066318975)
(209151625439330, 34376032998628737907295)
(989978630755400, 38947259601397055558375)
(1119915446189750, 42977966010216237307475)
(3840854243430050, 234355065188019636758975)
(3153193539638450, 173676878795099877156575)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-24 14:16:45 UTC · history