curve #1088

y² + xy = x³ − 990429690240960203866170x + 343844266388187332499781887080604900

a-invariants: [1, 0, 0, -990429690240960203866170, 343844266388187332499781887080604900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 138952056675401970 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 5
discriminant (Δ): 11105153909909660895030976450486072576491828715460883478057425567744000000 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 5
Faltings height: 12.7515 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 5
naive height: 177.3709 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 47, 59, 73, 347, 3467
regulator: 2676.98530619434164587444402063658258712725585891
submitted by: dujella
submitted at: 2026-09-23 18:08:06 UTC
last updated: 2026-09-23 18:08:06 UTC

(39632200740, 551954334123294630)
(376196308530, 156489276347919690)
(-387729217260, -818274779331071370)
(233546798100, 353936579560301430)
(276487413090, 301892365554581130)

found by Dujella - Lecacheux (2002)

last edited by dujella at 2026-09-23 18:08:07 UTC · history