curve #5540

y² = x³ + x² − 754393642505775022546593489099129770972182186100542700x + 224312117197112787363534904114582478496088716509191697361965884528995947709510000

a-invariants: [0, 1, 0, -754393642505775022546593489099129770972182186100542700, 224312117197112787363534904114582478496088716509191697361965884528995947709510000]
c-invariants: [36210894840277201082236487476758229006664744932826049616, -193805669258305448282094157372264630462283857557360551381287898273040968417972937664]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 542753340477481206662442076086222623804995483474041572187681148973270666756672402205343912589770599210963386344005343132032418419720
discriminant (Δ): 5740818610338788286183894247268574859345326307160457549527157565016929350890431917214459387493016464463908379714564668616733022605923574999080437499129592500000000
Faltings height: 29.9611
naive height: 383.7869
primes of bad reduction: 2, 3, 5, 11, 17, 19, 37, 59, 61, 71, 57089, 107970181507, 21843783571883337501985987056012574776931755825751880538802743715755508685212937964849630787001354665913
regulator: 145851285752866825834289676525742465.60325861277949150645791185272859443927531702742160657501219210
submitted by: Matej Jurasić
submitted at: 2026-10-22 23:54:45 UTC
last updated: 2026-10-22 23:54:45 UTC

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

(686953152007929754064565700, -5500491045930698977560464792405150076900)
(354540269006344514605329850, -1189318899350479009982055810929790432750)
(127833064536162161521607800, -11400202783000459806784019569263941057700)
(700705312008781689056460100, 6304152459133738844687715075289795297500)
(181497450971341099798284190, 9662833979720925639627492865297691642610)
(355687313347357445420079475, 991515865737642502539080521385919630000)
(781342739798285868220593850, -10577292265951359283637814018948255168750)
(86363978435465003517489475, 12641354638865092427034465205961018782500)
(355162964821618478685751975, -1086255354516456227503051880298255363750)
(-247766745913855294210051100, -19900145246966056093979369052594574701300)
(329308107117543434390038990, -3405232290859443999099531736888225695810)
(1345231405244458915699113850, -40544701159076120781069855449208915048750)
(3274023959587638873561132205/4, 99662204650429887905444537434424249904165/8)
(2687756596870496532287503525/4, 36474659803981397028806666830191038709375/8)
(-295940212757048698490966150, -20534091361589802601281429474898753128750)
(41492926917717075699347024350/121, 3244510594508051647517099251724741914940250/1331)
(60552007715908715884845112900/169, -246064001828941410258963935133606923185500/2197)
(-938009783071821673842866150, -10325756105693178779563655658821305908750)
(-830594195278059406948471400, 16670068832693325344582392134379856203500)
(-816776123734494996366187400, -17192803764725425882770175229829918862500)
(250337024820262066513620100, -7151764437554842261627474934047858042500)
(705422541905723872220571850, 6571063891509876030691123795597046046750)
(1067848892801081073316132600, -25227031870057252403745977475565650217500)
(3726206004627560383179945400/169, 31661929284053575498973478837070402065304500/2197)
(-1853357480701326837607424882600/8649, 15599721135055526679485035620838240541084217500/804357)
(3325370577236574307335082945/16, -559770704197472218100112923202017109991305/64)
(3955792499004640319251619230350/6241, -439400432362397316702574592215777778673918750/493039)
(13881554748284177617191993384100/52441, -78900277248555607072728383698583239567130347500/12008989)
(100981848535766948674309196085017350/819047161, 270505315339823663861536160015446462446163709540988750/23440310700659)
(56726722748713760374300961699149/84100, 115292630320047590595938116084196925353075081493/24389000)

Commentary

Specialization at T = -6039/29548 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 23:54:45 UTC · history