curve #1090

y² + xy = x³ − 3913976067656937637459249967383835x + 80614222594310898664080091661625700445673557913297

a-invariants: [1, 0, 0, -3913976067656937637459249967383835, 80614222594310898664080091661625700445673557913297]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 6580537988822228363790 ☆ record for ℤ/10ℤ torsion, rank ≥ 4
discriminant (Δ): 1029958981973062046086433480865385408697349408756911021069398678111359304410195548643388293120000000000 ☆ record for ℤ/10ℤ torsion, rank ≥ 4
Faltings height: 18.2977 ☆ record for ℤ/10ℤ torsion, rank ≥ 4
naive height: 243.6632 ☆ record for ℤ/10ℤ torsion, rank ≥ 4
primes of bad reduction: 2, 3, 5, 11, 13, 19, 31, 41, 43, 109, 113, 2251, 53279
regulator: 35741.23869187988833355075333463466964826814821
submitted by: dujella
submitted at: 2026-09-23 18:23:59 UTC
last updated: 2026-09-23 18:23:59 UTC

(8185642345602334, 7008872315854122124478833)
(-12386639730434786, -11278065707632343668729487)
(-71051466385703906, -134428832419254188216207)
(145126829591796568531936/528529, 53943123228441855079366471262433889/384240583)

found by Dujella (2005)

last edited by dujella at 2026-09-23 18:23:59 UTC · history