curve #1392

y² = x³ + x² − 1012621607539704052249922825514565569141039491117265x + 12461776334855266276578824086166969624861737049090409086979777257135259525363

a-invariants

[0, 1, 0, -1012621607539704052249922825514565569141039491117265, 12461776334855266276578824086166969624861737049090409086979777257135259525363]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

920927557845775831402090644065394792155032280291046315934115821048166717025673513388546443490398395644452613527240126103722536360

discriminant (Δ)

-633751702403398857129279559159875339571183868575790146649666046465552112684396059563803625992107208961050278740830647379716588934627307482301076780000000

Faltings height

28.1632

naive height

363.9562

primes of bad reduction

2, 3, 5, 11, 13, 17, 19, 113, 167, 6867690488653, 1093633223075749294349, 64120054681739758204026587033021, 1406342504656471182930912505056122718958699056219377

regulator

13044670916790444314622199923259632.9160076984200883430394028971857070541489625899161383192414166

submitted by

Ritik Jain

submitted at

2026-09-24 21:25:28 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:50:20 UTC

Witness: 29 independent points log in to add more points →

(1204525054221706983031371291, -41790127716836052046541168579977803623910)
(281942799120791569724531727009457874150888548975401/8335974219931830633045481, -3129154275503799523229936460619104025523793381994615878088261961266461893250/24067697496586434274992250399410671371)
(1577677788307294042549622771, 62652700756380024466473359207309857685850)
(85925943374050398855141857, 748241642502184311719667135857129389350)
(40648361724502848156259203, 196120423525849621203246743578634812698)
(-986279855782993813244700231/64, -79988557132480671340400232056814804551475/512)
(7234376931320127518079151174/729, 1146035446156153745847182123751235573164815/19683)
(-536672303875386021621826839/16, 5966135324623238553084219380116920404925/64)
(217262317781012522808720174271/2025, -97245762402068862768237649841726181389619994/91125)
(21520879147373255445747515409/1024, -704973522462795174308401642050859913410695/32768)
(-126389160617591641683392881906/4489, 41077157990166094771572064564382673669172125/300763)
(218089689621108666788430371, -3188203872802095721024648108006824586650)
(78443857395857666996792109/4, 96488541370592822278028098106025348675/8)
(4994663931409775853542940286/441, 458007627385793448128994545254410820987325/9261)
(-11925711241415245207226679, -151135382023465610743755764842794755250)
(17675225338575340618825071, -9243476324602107842332150067341739250)
(-17907938365484224760090679, -157647609213180151482360292099166940750)
(128202252581437514797023202446718816775383441352162334427/9738933403568505918058006749009, 1142404378850156110708741346300483268156614813827458446538902855428765956041382524746/30392546798670920484933482010675622600780495527)
(-28181246355348715539651780740140280675888899218/1007877992492958612169, 4400670955015644693639827958635405755208298743922776814932079674580531/31997197607072335619469977970053)
(-28042112564506149323873186400672408779031591/786992747463497689, 40129207781643286684807084839061714390424235117509902924314180690/698161820164454304081043613)
(7088652908144329413270708634692861933333420808388657493211889649/376164510381178450707165972679411508089, 61647284318673704311751392462444045250906462249115989850795778109972709280557573343421142425670/7295695990871289678785466005504421659944579661195177007437)
(245501591496451686381908616506268391421876951378930082586205856997620291/13325990977822021557735422654805616120339184401, 11830240905701995692366166111497787418746380656157132420179934692604752808520973091739561281049069757715210/1538329159654251151815554083162619548137465112725991012010742816505351)
(13838864347724169624147241531399279785651026187708048697460303061/857017211778396311087908392037600785316, 449331146252828751761829409376746880555682423481417744605739381147501817792892238520550327687375/25089055727188019900854032611994557803119362275324261428136)
(3074806950801968931089350898101977868343137/624371151125187216, 42994327689770472006876737605758928378040572970314831461931925945/493360348980946378265516736)
(45521713578381536437487788889151897135106928240041/4402026184071146095138041, 513903231859578336754120583735649808168573124483140491682332659672326647010/9235893837130191690788201816533352589)
(-49542578601004725379894468761/2209, 16047766811707251768808399525919364093250350/103823)
(51917846439456272893326809510839397444591/2723925428355121, 1313692912721833270903121138445250390540746272555184248645250/142165043049459496984919)
(1089615344483982003140427601986979275052417671/83369112278760000625, 29082098772904101247337831000407564870429716224173453054195354073406/761215750283143033425667984375)
(7451743850317747943782362967459910817/314914013584, 7392287580332536470961175330921790504102875455107155481/176720926830960448)

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