curve #4539

y² = x³ + x² − 21496024898202082543520412297184687714385x + 1205655490570854338247321975507171134252299971071185872419283

a-invariants: [0, 1, 0, -21496024898202082543520412297184687714385, 1205655490570854338247321975507171134252299971071185872419283]
c-invariants: [1031809195113699962088979790264865010290496, -1041686343853218148251877042008878059766521053747093783832003456]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 1419644640685810917871258182520976419367660474962862258456283696764454267322048018911003187080 ★ record for rank ≥ 26
discriminant (Δ): 7745837029876356633573405350606859484037883381068515437447484357046423620341567130657033370398409442324364340959380000000
Faltings height: 22.0291
naive height: 290.2197
primes of bad reduction: 2, 3, 5, 7, 11, 31, 41, 43, 61, 71, 103, 811, 823, 140909371, 67005074712695341913750705823789377329976438766104267439249795421
regulator: 160636163356694673325058360.722009827781152095230605319533585409285045071366031640664153998
submitted by: Matej Jurasić
submitted at: 2026-10-17 12:06:37 UTC
last updated: 2026-10-17 12:06:37 UTC

Witness: 26 independent points log in to add more points →

(95398918270568730931, -152246830910083858785471070590)
(77657590962546670111, 68232887177824775695300114950)
(54921515182549466326, 436720733347927745627915988795)
(61901285353682021311, 334985602088002934076953398650)
(888849055894225720669/4, 21764465426207045214182999845125/8)
(93559703148455209366, 116021449816479123841747821285)
(-118754649670229382389, -1443485759970050824104375709950)
(103121091669033635611, -292484963332947253561761168450)
(-166945871167012040039, -376021838676916213051380155850)
(385349739227915150011, 7081274921390118525126780402750)
(105196926215358118611, -329378662515116975462173981950)
(79170131051576953627, 6603844296088936253884855230)
(-157265268532498648409, 834680564459372972543930183610)
(99877823575069900627, 234560209274547082194249372930)
(-2069675447943614175671/64, -699585578355062694722238094177125/512)
(100505962207644052711, 245830469264411132042891022150)
(154440280974126882001, 1252789734564218561241823323570)
(260579175617852927361, -3646636491309139231465606475550)
(6389783963052544478258839/66049, -3012881320517877617118906634058547450/16974593)
(95170642371413276011, -147879811385394559734261594750)
(-346707652786816318931/4, 12439088573706009893161404337725/8)
(116882872070106796711, -538466418104984108910288097350)
(1996969562697052611886, -89005441259991649778263422345375)
(16904743999704385043059/169, 521258574922004804399038353302550/2197)
(69774837905262585691, 213247719933613497691806725310)
(-212684011874664516554441/1369, 45178897649274009721084052446512750/50653)

Commentary

Specialization at T = -3770/343 of a rank-17 fibration of X1152 (one neighbour step from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-17 12:06:37 UTC · history