curve #1173

y² + xy + y = x³ − 1742907593966990756845614x + 884438686985072950763948120250518212

a-invariants: [1, 0, 1, -1742907593966990756845614, 884438686985072950763948120250518212]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 106915252368321342649355608110
discriminant (Δ): 922410239138031366847032961159018548373494759561961888848903320514050700
Faltings height: 12.7070
naive height: 179.0664
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 67, 149, 449, 463, 647, 54877, 67057
regulator: 9983947.5691039300861795064378046124750196831040142891959
submitted by: dujella
submitted at: 2026-09-23 21:38:18 UTC
last updated: 2026-09-23 21:38:18 UTC

(-75449078194, -1007725103207297976)
(820809034388, 82740042886701567)
(411269065781, 487029241050481419)
(935988672731, 270356715099523419)
(263042753099, 666468018565637865)
(916824173531, 239061498026206299)
(2928006134039/4, 233685892742150397/8)
(1095944366783, 539110935117474009)
(1161370455566, 653231456289313224)

found by Eroshkin (2008)

last edited by dujella at 2026-09-23 21:38:18 UTC · history