curve #3542

y² = x³ − 1046682249624848681626383x + 414760695328933343023170602584800018

a-invariants: [0, 0, 0, -1046682249624848681626383, 414760695328933343023170602584800018]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 4858973778553085764197571571656035582930144528587190763320
discriminant (Δ): -927504287603275413213017956819491381103276817881526674818197850705811200
Faltings height: 12.6408
naive height: 177.5492
primes of bad reduction: 2, 3, 5, 13, 17, 31, 43, 173, 450257, 588183794861598519206262487911904153965919
regulator: 2539135793769485108.053735397754625813935954542740100252615283034500988322989
submitted by: Matej Jurasić
submitted at: 2026-09-28 00:32:42 UTC
last updated: 2026-09-28 00:32:42 UTC

(526888429299, 97704515096446680)
(628939591989, 72438142824039330)
(4096204133071/9, 4879440724690328680/27)
(393920990262, 252144369316822320)
(560823546538, -64409444664655906)
(-124274608911, -736829290488680370)
(154840952169, -506363350337410410)
(690445993869, 145703651629837590)
(770385539541, 256185339788783106)
(-1181535145229, 44716934876399144)
(4821772693069, 10366854006611642410)
(687243686019, 141501908640044160)
(543215951731, 80500331512102456)
(605524197441, 54685447143095106)
(3268214118501, -5648230210847400306)
(1281892911587541/2209, 5479783539588055534590/103823)
(39358931651721/64, -30966556035896805285/512)
(9418613718203531089/11015761, -13916760035849507514201233230/36561310759)
(17999517621746874/212521, 56000270600522660888408790/97972181)

Specialization at T = 2/13 of the rank-17 fibration of X1008 (equations as in curve#751).

last edited by Matej Jurasić at 2026-09-28 00:32:42 UTC · history