curve #2031

y² + xy + y = x³ − x² − 12622269502860390099380505x + 17129189830354371141956112739571781497

a-invariants: [1, -1, 1, -12622269502860390099380505, 17129189830354371141956112739571781497]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 269595394580676263069520550
discriminant (Δ): 1951331353645855386016870948362763093041664655914800673844407146625600000000
Faltings height: 13.2706
naive height: 185.0061
primes of bad reduction: 2, 5, 7, 11, 13, 19, 43, 47, 89, 103, 139, 179, 313, 647, 3037
regulator: 7182185660.9059275897427986440833908935788923397829248400
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:04:12 UTC
last updated: 2026-09-26 05:04:12 UTC

(-12299838863249/9, -152321312556029792140/27)
(9512946998639, -27530703774203456820)
(-3274423418611, -4832386192083634320)
(-500310451000969/529, -64635222298865987792940/12167)
(-1356372026695, -5635095092227179594)
(1588550240375, 1042483828218058716)
(254738843758427/4, 4059572660491024659093/8)
(3772308154990135/33489, 24289851227290692695672276/6128487)
(17012019774490681/15129, -3884577671570708145155440/1860867)

2-isogenous partner of curve#1934 (Voznyy (2023)).

last edited by Steps Unbounded at 2026-09-26 21:44:17 UTC · history