curve #1123

y² + y = x³ + x² + 21684687816792871940x + 536323633330486820975424434082364

a-invariants: [0, 1, 1, 21684687816792871940, 536323633330486820975424434082364]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 10634268180369499203615
discriminant (Δ): -124261793789513124036664880282916019565721748754505638761521370696875
Faltings height: 11.7450
naive height: 164.2477
primes of bad reduction: 3, 5, 7, 11, 23, 31, 83, 107, 137369, 10584869
regulator: 231244.6022765925297056359090335952500001130069341371
submitted by: dujella
submitted at: 2026-09-23 21:17:46 UTC
last updated: 2026-09-23 21:17:46 UTC

(14602668701, 23232609206364442)
(-26663475064, 22733000003801587)
(12940574036, 23211446619966412)
(-67481833414, 15085147779935887)
(25151681021, 23511277519972357)
(43444943771, 24885064864904107)
(1428145783223, 1706872570530131119)

found by Dujella - Lecacheux (2009)

last edited by dujella at 2026-09-23 21:17:46 UTC · history