curve #1089

y² = x³ + x² − 5334348061487201120280x + 149721135899592401852463095048100

a-invariants: [0, 1, 0, -5334348061487201120280, 149721135899592401852463095048100]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 104034096695931795120 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7
discriminant (Δ): 30687052802523286199676528074048015124225209792162750211600000000
Faltings height: 11.2653
naive height: 161.6990
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 41, 137, 191, 557
regulator: 88657.76679457180340864859429659441658533028276450673
submitted by: dujella
submitted at: 2026-09-23 18:17:12 UTC
last updated: 2026-09-23 18:17:12 UTC

(5359329240, 11013016898588250)
(33560492490, 2914994668950000)
(49198220490, 2522552201778000)
(40461341130, 355436590214160)
(16644351690, 8096013181198800)
(44116137240, 500611414899750)
(43529729040, 12840247642950)

Dujella - Eroshkin (2008)

last edited by dujella at 2026-09-23 18:17:12 UTC · history