curve #5539

y² + xy + y = x³ − x² − 283032721698873960414252271198870690998122233118255342x + 59488772278373606279049788898449975115116316314707646575503806005858545868575741

a-invariants: [1, -1, 1, -283032721698873960414252271198870690998122233118255342, 59488772278373606279049788898449975115116316314707646575503806005858545868575741]
c-invariants: [13585570641545950099884109017545793167909867189676256401, -51398299248514795825099017547125710612503721846428916062279219133467381276906286649]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 771057259303005757237615996423540170892979796856835346344825131022901071299347718061045432669229105793453623925691755104780257495130
discriminant (Δ): -77735669121886728178163621641158862253460110865900234239208412103262627789513713213651672687374046672594989567898793534179689169774698315390820671499973120000000
Faltings height: 29.6489
naive height: 380.8980
primes of bad reduction: 2, 3, 5, 11, 13, 17, 23, 73, 283, 1091, 4067375770337887063736194981195538021, 8938021109847908645230641237972911018899665844968485284831822673349700203245303
regulator: 109864075408753327285155361033946084.93037591599495773391561160661558167493309124813817235608747877
submitted by: Matej Jurasić
submitted at: 2026-10-22 23:52:32 UTC
last updated: 2026-10-22 23:52:32 UTC

Witness: 30 independent points log in to add more points →

(-258111444790961921718267079, -10739971170891002726499163763482518952461)
(287243653775768933605657881, -1374620617716000806272917487055321969101)
(-613937146554396853741404079, 1359635626102265516866061596088364025539)
(245551426728533191513367321, -2189824304065431650554696862473797530061)
(2979869892276222418598917421, -160237991786601508915397216018291079355461)
(1259274638751674073120537201, -41231008741164622469601877954757178770421)
(258820578311655601846954121, -1889967252584215696850046749522895936861)
(321764448553529680279475381, -1316030962685057742456738486736971101601)
(517307674929957385553885721, 7176980375691737817614476045706759756339)
(275721213297923939921138921, 1552925179544401345173799452960516043539)
(-16358713624892920387214479, -8007149667920258495650440906699047727861)
(17181142286187605969379768185/49, -628395080760240484211856484815008205158619/343)
(696857369737009086839774621, 14165323032836575399199839541638006475739)
(-2409216652633924873648613941/4, -27085044045664261819351498729925937070563/8)
(264814014701250407950946681, 1763011909686840013885575476854637945619)
(-61791316753208442894252679, 8760240138296672933667122986200018302739)
(-246742462195667360838961429, 10691250027650342748051006917694328284939)
(80348539379486051768705921467601/241081, -174736684508253525006532735365952007610075685431/118370771)
(1252740297462489061498079921, 40876895685115143132086767638621722494539)
(-62225402785896950701493479, 8766964159918930169011418171773655580339)
(12297386934843142704425460041, -1362446397453858824786888998695028520724141)
(8674982796485157108688880921, 806500370539039837231385429540988291583539)
(839184294075994350254410841, 20321199458307141075218116994988503672499)
(636723234870242607295783449, -11722344192767252937545159670648579423309)
(684645199183787660717227841, 13661321955159436916147623836720558658659)
(114567855234328394288301698561/361, 8754888311372473051117179687909696162245361/6859)
(10894444512392137935262470679369/33489, 8317577147885375002592374048581918914764999493/6128487)
(5914747008516142213182981252159/76729, -131240107762804408397071803575357652979182553113/21253933)
(15331933745041568116558057229/49, 428779236285405657380893459885207228410477/343)
(-1367250877336941823269266408479/39601, 65565214979952597361676353517433756568923708861/7880599)

Commentary

Specialization at T = 18321/14150 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-22 23:52:32 UTC · history