curve #2008

y² = x³ − 194002827815441878646956347x + 1030749813484458772329514114688113395914

a-invariants: [0, 0, 0, -194002827815441878646956347, 1030749813484458772329514114688113395914]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 785713583551212949496355574586236811508456240
discriminant (Δ): 8332693513712411792451141758692144036419300940769929997526407447964962400000000
Faltings height: 13.9607
naive height: 193.2033
primes of bad reduction: 2, 3, 5, 29, 67, 211, 241, 337, 433, 479, 1117, 1181, 1237, 1637, 1789, 16253, 2034421
regulator: 15877309263512451.44505463021102160919267839943140306666795182398
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:59:05 UTC
last updated: 2026-09-26 04:59:05 UTC

(283820970929066097180913/31646986816, 19664455245416442356270861916570825/5629872366619136)
(40721776567814, 246288507483743210360)
(79859547658310113/2916, -20078041157966097206025625/157464)
(3962416195847356069151638026154/456563842487596561, 265057481133085674485811962478113377945682310/308497942531327799780216441)
(35183281873490376140247446/1207288920289, -188194506605372030492850790687448351060/1326529225079183663)
(4901637282252118, 343170544992507896402700)
(1947986575029504369936698/222283017961, 199807571346388693548881579582389450/104799552195054709)
(2618538242555590680773743/265741281001, -1193105448552893746343293802860195050/136989896097296501)
(8668206128743, 635003250003468450)
(8884952993247764294851367/243381395569, 24782179787284211936707446381880448750/120069047545823753)
(142364309910838294439625878/12225938826721, 800442746824620509485526552100888941300/42748740889898406481)
(7315615302869638/841, -28708721069804479822500/24389)
(208022647465156567620652534/4968704025481, -2851658689507598014711507375804852320240/11075534426334652379)

2-isogenous partner of curve#1924 (Alvaro Lozano-Robledo).

last edited by Steps Unbounded at 2026-09-26 21:38:06 UTC · history