curve #1949

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y² = x³ + x² − 4384732162429896843769671712068813665x + 3539976250811225562728629191656289711988875801765859779

a-invariants: [0, 1, 0, -4384732162429896843769671712068813665, 3539976250811225562728629191656289711988875801765859779]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 20166670453232581302505390352279053584220250472252265697936471245359365286698003789876244470054712
discriminant (Δ): -18358245413073584198438096693047001168684666629890394646512252116851728101673681692004055673678640849612923648
Faltings height: 19.8540
naive height: 264.7306
primes of bad reduction: 2, 3, 7, 13, 29, 31, 53, 719, 269536208976268414426307214392965782709977541998673590653432140444281434340275111161351
regulator: 220127661428157093601042798.51203654762889968993117701953654545589819991733204520492412
submitted by: Ritik Jain
submitted at: 2026-09-25 20:01:25 UTC
last updated: 2026-09-25 20:01:25 UTC

Witness: 24 independent points log in to add more points →

(9919258793693935338553893999462395966978862601291/8015427543646591180275412958641, -2151618131416977292977452359944248387647176227773745339340740393219129694/22692902068058914318649678932195813021092892439)
(30898111626655069180783/23409, 816993567250259373217142360575478/3581577)
(25151931574629443713, 125717389181762136591599411190)
(20300005749013793655919/49729, 14952819343477103303707587231674118/11089567)
(239254134726583222639/49, 3404876428650842604881511624522/343)
(5660087187375150608731/5329, -110737768545440546443250921481726/389017)
(20039747944430443929379/10201, 1631524654614624205528437045708618/1030301)
(2396240313557100703891/2209, -25438495943207564197321283764974/103823)
(10048634765092198320031/2601, 882537998982893521053246777242654/132651)
(1013255849091868650865/729, 7116233839845488549967705675434/19683)
(196811442737539307743/361, 7855076078333086896782725632930/6859)
(94729056427318352755/361, -10642416559809437808757673746182/6859)
(1543223276719999067281/1225, -5338671801216189961801371271254/42875)
(4554150836595663991945/3721, 18746377490894648293682022910962/226981)
(39454047407977538710, -247478437612093950833369159277)
(54568817358435089110/49, -66939179142293389600365028389/343)
(4338585159179748571053366802649731/2783338717625449, 103064669457041593364559060577622576432988623577606/146841594377688005178293)
(957044716149969348630504667399/322811467225, 747247596542157195145899221673002792614934382/183410177275892125)
(64384141285186675267216780770583969/35743536889590544, 8238525662787563768131121140703450038329507475953063/6757659215853675087508928)
(13596008058392438276312818462437817/5546506112567161, 1132826900533151554311296596155151389543160405068606/413075316141138569176909)
(19946053293950748455126330205213799818209827621590020185894153943596242891453845257233572323/34207831872589443490316290342984965032674408275546202573909733888521993609, 217477399672922415354734143253014338697838920336373725272292165781829521928067185228983553615819149890151110180384319443992555526012180518/200072925974878376189013420096080803781848653952813288943898551215185241953844000821389043670654231959853908773)
(36906126142658797061092815431483442479539815542695/15754521690206214908860990373689, 154743645297953232688096428236728104466720196826573415994012546474773489074/62532794008274380521254262779388554324199625363)
(13906258334326046536661993830696314023568463/15481385600283657949750249, 34786620653079451604086781523463598432784568095965979397714487202/60913666586513283908057245135586477557)
(-138830627327705166937292265833178845809474045939013342528360845579465015335437/76968081773567097881005355456407869141149074067876490322201, 50442961838507514616643641531645027631429815368181331214717116512630772368048297778029429345584279197206810698380790/21353348819576867453966436523302513206909060695707969033134937667963686882714424335357949)

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