curve #4119

y² + xy + y = x³ + 430538995603587596075735914707189109975218442500581616207x + 4206571925894845581175768135604356324175399145322081497415521143000583687493758917608

a-invariants: [1, 0, 1, 430538995603587596075735914707189109975218442500581616207, 4206571925894845581175768135604356324175399145322081497415521143000583687493758917608]
c-invariants: [-20665871788972204611635323905945077278810485240027917577959, -3634478143973146582135863669131165056404086554640825427908092651634288578134565828446589]
rank (lower bound): ≥ 22
torsion subgroup: ℤ/2ℤ
conductor (N): 2035380499394781053410535073119755867113480721020446687608912956074864478189031910388141364236880110 ☆ record for ℤ/2ℤ torsion, rank ≥ 22
discriminant (Δ): -12751953633025813552068403253313313912552392110390944973970655062034241685216187799377597956563902639153911046857157671382497444640011106015828686458850494861007879729652500
Faltings height: 31.7095
naive height: 403.2307
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 29, 41, 59, 61, 103, 109, 163, 167, 173, 191, 199, 307, 353, 797, 1459, 1549, 11059, 20389, 72227, 508531, 5809451, 117291869, 61056459470068873
regulator: 9551539763033768133089539852.880383443462435353384900993900855014478562794677991972
submitted by: wgxli
submitted at: 2026-10-09 17:52:32 UTC
last updated: 2026-10-09 17:52:32 UTC

Witness: 22 independent points log in to add more points →

(-8384971709388650173069187251, 83583063553756919010177649988681035333170)
(-8394787891911479326769063626, 26210555181210238506364196725844463256170)
(-8394979117188946175374358486, 23753610121056140852937432843031449266150)
(464471941353622486284418784, 2099201136500902827563738830236660621658455)
(800020238691507081503960369, 2133430072625512254801211641809701941853290)
(-584560731486932639976877858, 1988641743681754882513699039069453173628002)
(-7414110819473860799959285141, 779077372148631036655570844341867782637860)
(-7510945035366901694535993541, 741007775225360867951958706484272995125880)
(2386197178903036299782710589, 2290744359146671273111689100057968368798160)
(3105462961975177773468382184, 2360835361759333299181212569263411302397335)
(14146627805323447458485424859, 3623309280522550888805657065303315859892860)
(15195582200542970740522065449, 3775924979240907435926984901260268163139370)
(17475158341531080349827896018, 4131209647959381562798856441922478718422863)
(23470579050500523783817493819, 5219268559600762279500451612734044966142840)
(30352678423365000367527810794, 6725923996333477395511654555172374574258415)
(11235404013777179425283952382091/4, 37661267427689820631713220525287294914084539035/8)
(550074140033974183671474417049/81, 1988923830336103190331324661973538653809385900/729)
(-8064000020247182828353603643731/961, 1618612049682641036271057429043353082862332320/29791)
(16495490677804513427764175773379/841, 109606960567467579265083949826652847724042727060/24389)
(-606979889554621831381224304719499/76729, 11750632701949364259581335149453391741497395874570/21253933)
(14874033420571616465873624452902563/29929, 1815635864443808349713147636774498460187695901165140/5177717)
(4487537904920428503189541502351066/635209, 1395738341916036742315193565485209619345751897127710/506261573)

Commentary

2-isogenous to curve #4118

last edited by wgxli at 2026-10-09 17:52:32 UTC · history