curve #5490

y² = x³ − 145093783390266873995293538084509332x + 21754002519200929025794282370420681649067086612662244

a-invariants: [0, 0, 0, -145093783390266873995293538084509332, 21754002519200929025794282370420681649067086612662244]
c-invariants: [6964501602732809951774089828056447936, -18795458176589602678286259968043468944793962833340178816]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 4002375907755194716463833522635881781985695177847928158471121787987276566645580360 ★ record for rank ≥ 24
discriminant (Δ): -8947392557084668031920342633899369726515586748650495161082468506174814344402447172983762856447858136800000
Faltings height: 19.1126
naive height: 254.5464
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 37, 61, 73, 79, 661, 114569828081, 6922807401479, 10221591313915031, 4479641215015280468563051
regulator: 588731104539973746259079.81542503441923369892919204474397094332091676027576530656032285
submitted by: Matej Jurasić
submitted at: 2026-10-22 11:56:08 UTC
last updated: 2026-10-22 11:56:08 UTC

(227468559432093978, 22790226870593134241750370)
(87474804433911438, 98647329023779350430201950)
(1855781392577329488, -2478641322706559901776626650)
(198423247929151698, 27862165821984365040435630)
(194859605098594938, -29664055102825431838547550)
(192389282057871078, 30992588297255263780294830)
(321316951633708938, 91143541473467826328344450)
(652324998437221338, 452424788818765871022712350)
(92709781652230338, 95389935115429813326267150)
(56624477129418378, -117131121994126961792364930)
(305897802766963818, 77421253873928794625283390)
(-389386549275463287, 138607531017702919867606275)
(450173149826344488, -218327520090901032644619150)
(5712031252460746218, 13622082694612199235789673410)
(1177642784147314938, -1218232510738024934889049950)
(10632382655652037278, -34647423966847613824163081730)
(275876929631461390, 52176992659462906351944542)
(21183344958058507992/169, 163474230806788490333072143830/2197)
(289372874946548838, -63236979242662125468704850)
(168910593292167738, 45445328701841594494864350)
(-364732834865693562, -161722124468488950361074450)
(16185944543554626912/49, 34075031667669203109913678950/343)
(26170622835438958138/121, 29463773681768526180271897370/1331)
(-19260086503163351383722/43681, 23616014343249608239703962122450/9129329)

Specialization at T = -108/71 of a rank-16 fibration of X1008 (two neighbour steps from the one in curve#751).

last edited by Matej Jurasić at 2026-10-22 11:56:08 UTC · history