curve #1906

y² + xy = x³ − 584575908845266159343734320420x + 168678688516060008059769081909630373379312400

a-invariants: [1, 0, 0, -584575908845266159343734320420, 168678688516060008059769081909630373379312400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 169457189601503603310
discriminant (Δ): 493578371416484323709098843762396601317153952102088257894857952178932493560422425600000000
Faltings height: 15.9979
naive height: 217.2357
primes of bad reduction: 2, 3, 5, 7, 23, 31, 41, 43, 47, 53, 313, 569, 1447
regulator: 69946.8624013647171541713179234612890909937894120
submitted by: dujella
submitted at: 2026-09-25 17:59:11 UTC
last updated: 2026-09-25 17:59:11 UTC

(683483555143560, 9403182830726308713180)
(358860191188260, 2260953171316277017680)
(495095124921240, 784422017626985956380)
(156430788088505610/289, 16180653055535639419514190/4913)
(576710495535576, 4833078565542270063132)

found by Voznyy (2021)

last edited by dujella at 2026-09-25 17:59:11 UTC · history