curve #1821

y² + xy + y = x³ − x² − 35461906826777069684716408079028742008397112x + 80299166509927780103996562882827637108892126567643321591456462011

a-invariants

[1, -1, 1, -35461906826777069684716408079028742008397112, 80299166509927780103996562882827637108892126567643321591456462011]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

842401411790515452226757484505874411309526100950203454023192956477698309338930299081602915992071926580487807610

discriminant (Δ)

68563504726587859461460574156292242879728809098668645923657662466662162256756173395116655066385631820730151332962341520866432000000

Faltings height

23.9105

naive height

312.4447

primes of bad reduction

2, 3, 5, 7, 19, 41, 47, 5171, 33217139, 1028905573842178911678956713, 206647872965550981311873182947544909925877750981613684968092854027

regulator

1696601656655961983980168611950.6722324757367032899560194407513678953848767711771312803241410

submitted by

Ritik Jain

submitted at

2026-09-25 15:24:57 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 15:33:40 UTC

Witness: 27 independent points log in to add more points →

(95659858801241450288339791549/24039409, 5524664739069816268926498200647587755288303/117865222327)
(2837886593830933001581, -50174703918451950129516789042391)
(9943414973993405240539/4, -693157801702368630339329847712823/8)
(2974873229850148025581, 33641235777903376743596559672809)
(12215435959035626275010221/5041, -33184271188835891754124996075173170801/357911)
(-99258507069953904071651/121, 439103345782674709408791740821866619/1331)
(2970025437816982929057989/1369, 5901916558572734862978595429410963877/50653)
(876116587776053152023061/361, 633500075418405109106557806784723811/6859)
(14498493494681791527871, -1616734304574884267625437407024921)
(38467017065078176638962087883383993712926329762958281/64518086067932884894514476481401, -126269476508809095827796433759454851587664798238603388106804198210466393651032141/518229597758804220290794262278282291908350300851)
(1130269505068908642019309/289, 185764253910646306633977462453357817/4913)
(3829308832463914205779069/49, -7472274137446925917017859700489724913/343)
(3120741260206424832481, -4971018356435312225892534383491)
(16105189522328795712822229/2809, -38087797037761294801447294146910773707/148877)
(-264199176899993402078325839/116281, 15313104785529466509648621885594701579389/39651821)
(1123151462595301196910601/121, -987895801220842368309843834788588621/1331)
(11998847922549577661685650628469/6904446649, -88731409238926889084394309458019753432674567387/573711185405357)
(2644187787073738687893999323240005287701323343908462603536029243395529528063988209059/1096308792302057981594253095953312343944898780866906863793286169, 3405037077238786865961562745837892968422320465487995152323973703847730719028218715381024892163355543339202853994030470639664183/36299391569429944933853171889391938759149374722889507192830708469178778409838262423765328579197)
(-11290190577559391242438459084051107349/1653939987532921, 4402870120403465318071342506979023913972487989664673679/67263524667320590488781)
(-28347574079460546613066778714533470413016333251/7476110125877480861429569, 8182908958219924832975870700445846816893045513840390056088462821404697/20441536425723393331664791946191510753)
(1487041067488074355209732123189377845228586303078939134964586555124540301/360111350343990462016635807078747629538421155333241, 446912188179486155963962273525612104588223673028165488799647247679638413341550098051722183499651133703308261/6833689077353106255418391830844877626415210946271466580813489284439123523789)
(4744950760900884978152279843974744565178476368320721902477956509/2307631174505213674470446453987593011489889, 444465033552522868922391640824358262110791495596260055075413864059717270713919931560651858748967/3505496969630086274017863703054803720564924291746319508250388463)
(4018734949205522161649812604878860969042294905390497447943840086731304145841093702882631103463009645095/802358483723287936537349415533459527000121266008185678031064387335060580044208996, 3825585594991634753047229478117161643945205487764973917458364197387189622631800372601581853954161399357917020049510840117715983821901069193913075248397363/22727552700121172127771363257887303525336350306200141820205306518277495955103573523201925739453983960332195171711737997544)
(41252456305485655555086922079663961562642520820410227412858891396165486334296205210207252532174379639869/13980831673690433000576433372081975942556241751205567370036559595769376907669068049, 60803946707144326565082815307819153935974611688249271878128642434072071643885744165307870723173254377076937031913087597067105326151992975555763745408720863/1653101463590745490882683064614088805981363543706449424073933133198345079348301636165873242358205885239805509290485493254407)
(2281863428498458523594667027514962461/602388055524025, 265913568419003919990485052289673660081098966115778931/14784768467619182369875)
(1598865566786967266195476887286989718805919187725948183364305534491850301/321791152375009879705147317339890050385568539229841, 944368216814823478634473250928515767459387013394854959160421078853081177366635487489724909972118495045903329/5772462875912102863705369674031297032913949325047184240742509670919527170361)
(1420262067234768424532658046681384352915082895283991275472344730956561967565339204961276730540593999660033182741/2144164181160407404334704697731650208695521960290674423004262631290447060635997774792694681, 750250801557527685140077028697796109125985847602833383780601543059713915620750201582361920343512947729883547770934257718657766175154752703856158758323282653614916443381/3139692062883492644035267178431629760284430079633578226452945216641234780283305091436966887653192611293042831567752883687919560588592829)

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