curve #2012

y² + xy = x³ − 1943384300833178732461426488x + 32972855024330273604877544427050535158592

a-invariants: [1, 0, 0, -1943384300833178732461426488, 32972855024330273604877544427050535158592]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 7957055249285451655668179172815993925972577312050
discriminant (Δ): 64017590963141777831068372626441510905887342812954988681101566987729187204000000
Faltings height: 14.3601
naive height: 200.1163
primes of bad reduction: 2, 3, 5, 17, 19, 23, 53, 59, 71, 73, 79, 107, 331, 601, 3319, 5813, 214519, 3616013, 17506729
regulator: 592122795020837473.4771670028963579317996659890058823407526128528
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:59:14 UTC
last updated: 2026-09-26 04:59:14 UTC

(70432943161589043680745021307668/33669611688681721, 590973593173366106565615747402365567744688622152/6178131694034665870607731)
(7163954005169555170510673076/278695345377241, -7611594507594317720649622978100381361720/4652587752631720762211)
(3591668754835529571208928859992673/960495305404293376, 215235729591751254412018157548769771496670482644055/941332102419937486841114624)
(267909348100745573381085869328/2151260332385761, 130950549366194933293555620210611096789966520/99779070484670335644241)
(167138722320721733569339543692201/41434589171814400, 2160676687089733067431742075350124063667947904459/8434212826717979574272000)
(429291724949346497748/16752649, 16284420940681734276505153668/68568592357)
(64209563537240949564478992/1349107803121, -344346263812358955623534771229150433656/1567003553510875831)
(1413008858507537850974013328/31807468115721, 33227780925701075751099486788577686859112/179388108561192568731)
(513473484084622169855458911369/12109803424880704, 218173010326278868484478041354224663160012847/1332617892699062725124608)
(716351693835048310207203828/15956166063289, 12129022663411336702423875806988279581112/63737176594630986413)
(25641858625296, 719411816662455480)
(5384916430939383914733842868/49319565338521, 366944951090452737162571010822308434802500/346360900944146555069)
(6665211911444682079351238928/253330802144161, -29810648450036285707632350845360571355720/4032106525992457671409)

2-isogenous partner of curve#1926 (Alvaro Lozano-Robledo).

last edited by Steps Unbounded at 2026-09-26 21:38:19 UTC · history