curve #4026

y² + xy = x³ − 15238762514989549071586355x + 20751154116233111225496786513096365025

a-invariants: [1, 0, 0, -15238762514989549071586355, 20751154116233111225496786513096365025]
c-invariants: [731460600719498355436145041, -17928997156426505289730302794848413599161]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 2684506118155302960385266241019671454852597562307962510
discriminant (Δ): 40455901908196012820569381215253175459743119005788528179768495122834764800000
Faltings height: 13.4348
naive height: 185.5713
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 41, 76697, 6609633666534888625281810452765988139621
regulator: 888224184097647.30683684210135241118388225940474392602103715858014661540260
submitted by: 7fff-zip
submitted at: 2026-10-05 14:05:49 UTC
last updated: 2026-10-05 14:05:49 UTC

(-4310146633970, 2522162367312024025)
(62195903888536, 489558210663389164417)
(2148262868727718/289, 87641132346307392858521/4913)
(72769717517372350/361, 19626602069948440507805395/6859)
(614971828145470, -15250149811892125197815)
(413434024195588495/2116, -265780579400090308536220565/97336)
(5660992551310, -10765760429797198055)
(2830063948942, -539635747556375783)
(1248275115311230/841, 28884287856807468348605/24389)
(-535470695586950/121, -1642033472834658042145/1331)
(4033034425363390/2809, 201489583290071147398565/148877)
(73060013576710558/2209, -19615509425393467794874009/103823)
(730779454332894910/249001, -142022308380390222988810445/124251499)
(190683582919630/121, -1073165614156894802725/1331)
(329882611525440/49, -5125445690839480776615/343)
(-5959001268785/4, 50689220016649177385/8)
(143376667557782290/49729, -9806313645521316300748685/11089567)
(21929859030760, -101158534638487791305)

D504/X1008 2-neighbor; T=1/10. Pencil C=P+O-F, u0=t-c/g. u0=(-93282*T+(78156))/(-225701*T+(-180536)).

last edited by 7fff-zip at 2026-10-05 14:05:49 UTC · history