curve #3816

y² + xy = x³ − 15729824000802676398459658212651180x + 441918375058252089931254114033213397202329431268752

a-invariants: [1, 0, 0, -15729824000802676398459658212651180, 441918375058252089931254114033213397202329431268752]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 1694102883739326127269684178211648231588071568524634294467969544121623015670 ★ record for rank ≥ 23
discriminant (Δ): 164721208674624898893720793564837787550267918189683074153557626067385347554600704419405135849701376000000
Faltings height: 18.6965
naive height: 247.8362
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 43, 89, 82393, 2501201, 282726525656474594672457937857027854175963383400184883
regulator: 2587270286643003580487.32168202239815045290734263853341767574222345233362256907656203
submitted by: 7fff-zip
submitted at: 2026-10-03 04:56:25 UTC
last updated: 2026-10-03 04:56:25 UTC

(28819392515473014, -3539853438440797897466502)
(17934576544290257154/841, -262873649597836079925090711258/24389)
(-5130532527346247784/169, -65596862239615859421446090844/2197)
(116288116225978872, 13611846289056749406834420)
(194529041990972094, 68871553507997994492269328)
(4177460987868825384/361, 110904703973797730279686964652/6859)
(502808339677102851/4, 169869055065873950408828199/8)
(46713512536558054824, -319273021585289384599973260092)
(82208385210026304996/289, -676938780145024982604272853756/4913)
(24491618821997964, -8447517946500029400096912)
(-140316927113310171/16, 1540249360634321001254503767/64)
(135292971010412544, -28110704961416102704894572)
(32542141701156028851/2500, -1933952672216287691545138635801/125000)
(-11231234891384394264/169, -75908362266201703818806549484/2197)
(56768250414582655184/121, 413101011097383831355322571028/1331)
(37358940411097010328/169, 193625184414219263692714404516/2197)
(8579883939655293993/64, -13951806640519497605562903105/512)
(23892391857404784, 8929397604438625654275348)
(99633638448825411/4, 64778945681394086740741059/8)
(-28172495610231336, -29371866771410473685368812)
(2697556387164936024/25, 120526540534385828093650308/125)
(328312612611190389/16, 723481517898974445269379357/64)
(29516668594300524, -1828193140800170870539632)

X1008 at T=-215/191.

last edited by 7fff-zip at 2026-10-03 04:56:25 UTC · history