curve #1119

y² + xy = x³ − 756828185715435657801375588494450478688880x + 253401847133358152315350001760510755926602193561212158650118400

a-invariants: [1, 0, 0, -756828185715435657801375588494450478688880, 253401847133358152315350001760510755926602193561212158650118400]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/8ℤ
conductor (N): 4180423832258126825781263565690
discriminant (Δ): 4379977074164100708110930543124522697442386248454073918451321129632676644386963220229077733305301134974851591643161600000000
Faltings height: 22.7636
naive height: 300.9035
primes of bad reduction: 2, 3, 5, 7, 23, 29, 41, 43, 53, 79, 113, 401, 719, 142159, 872959
regulator: 8883351.0224025330218240563898228703850745828160955
submitted by: dujella
submitted at: 2026-09-23 20:58:20 UTC
last updated: 2026-09-23 20:58:20 UTC

(620360330455938117460, 4758091883195699130662218969420)
(497190314206408214800, 136962231152035964282861848720)
(4355219292628560802420, 282075815982149392450508425131820)
(490711380442247094160, 424022366175406313485509707920)
(-448543293347798650040, -22419392091058428164924864493080)
(1562969108844553330473522536893440/2684692081009, 13987784198174075611499325865842096055521336633840/4398876028809489527)

found by Dujella - MacLeod - Peral (2013)

last edited by dujella at 2026-09-23 20:58:20 UTC · history