curve #4111

y² = x³ + x² − 31474444001851270791982973540897505565787453814920x + 67517856203171228034687195311237442085272360909440950217132208331429862784

a-invariants: [0, 1, 0, -31474444001851270791982973540897505565787453814920, 67517856203171228034687195311237442085272360909440950217132208331429862784]
c-invariants: [1510773312088860998015182729963080267157797783116176, -58335427759539941021969745813549022494841307916853360766083830945142100142400]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 322603758958242647542220542271392585593818068317511565892515943705988412227992083496
discriminant (Δ): 26169713106406503409437335040206844773550417041478400908693188324983059302012591382128950956758778672915339487912491082771161981194392879220288136192
Faltings height: 27.3084
naive height: 353.5334
primes of bad reduction: 2, 3, 7, 11, 13, 37, 61, 71, 173, 211, 337, 457, 821, 863, 991, 1567, 1621, 1999, 2423, 2549, 2557, 2797, 2843, 6367, 13099, 14249, 50929, 59971, 247901
regulator: 43745363848986399021525.0312803211590130630918050640495073358051849197168324114
submitted by: wgxli
submitted at: 2026-10-09 15:26:37 UTC
last updated: 2026-10-09 15:26:37 UTC

(2850307569897503447310160, 981137464736469963707554442755856928)
(3015774015496106683503640, 161825676464728091810789146689665328)
(791030915039769973817008, 6566244715676214618864719542402330800)
(-788632437256580718059589, 9583795737884290905862583912126822046)
(2376454475923922448448024, 2478181750507014521719017346268128848)
(2839004603417421964102936, 1021759179373665503578962965523598704)
(3751058291001344084676727, 1494796416890006761705261451260480584)
(4362620328885726210575227, 3638431942357070993598092318144621166)
(4909539781127218500258808, 5597348515068365910132150431984705280)
(5994384732370004602572571, 9707834367133254548231114401949772054)
(-6074330178597338872395824, 5880178716600220122180979635059791296)
(6806210498338536073014808, 12984239385168978416245609288468960080)
(-3823897879000519687843664, 11487346754569022611914057036792469296)
(14636523168596039711834107, 52367850238268850582744914777962211406)
(15604581737375064566367736, 58104512212884725970353823624545887296)
(90378996586914815421502491, 857596258772835480130307308637285344554)
(13858605482905796003661805/4, 1941453034329231339231989452284692901/8)
(-8111485089186448992209939/4, 88726037392751183606211263492658660261/8)
(10836409575712425005541853/4, 11684124842969293932819654162464704077/8)
(322095226759204315479482968/121, 2144950860778657620838199210883185845200/1331)

2-isogenous to curve #4110

last edited by wgxli at 2026-10-09 15:26:38 UTC · history