curve #4134

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y² + y = x³ + x² − 2898759786060307206242526376767549908x + 1981568866794539643948043306190327485279375950619198694

a-invariants: [0, 1, 1, -2898759786060307206242526376767549908, 1981568866794539643948043306190327485279375950619198694]
c-invariants: [139140469730894745899641266084842395600, -1712075500910482253205952234933811422679228417844042045400]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 4054418761511849919790596938312542317650281517101756561636548408685521398398693523957582011027275
discriminant (Δ): -137403497046599822424829248478425235766135390370221831304324088164286447142702980025259398586056403234090766875
Faltings height: 19.8939
naive height: 263.5701
primes of bad reduction: 3, 5, 7, 13, 17, 37, 4243, 3017957, 169143408691, 25649873192796956042086858360177306397665306103857752304638902691859
regulator: 149390422158597293723008132.94142674366996369974588631333822162520919596539452715044134
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:05:20 UTC
last updated: 2026-10-11 01:05:20 UTC

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

(1719803183948895349126843573/1538914441, -22408792173415701653571731983153183152197/60370074605989)
(-1380497805469047052343929045758452483144/1351210682892338511049, 97794972239228678430290568896820749854017044155066461246154/49668907243750988979202921897093)
(1596176902621585163468774416/2722230625, 98758372710367575021134434477171551155411/142032382859375)
(-5011781594218476203/4, 15276842581275691528790041451/8)
(-17301630955509232071872517248192/9244573359121, -25934234615441791102481511064821065251094479307/28108023608100450169)
(1210891283860832327269/5625, -493346678886476876008713760173728/421875)
(228693544302723643134359532454066/135542846590369, -2171653144009723077285197970530647960625918529926/1578028720802047333903)
(14197991921827524158979055747/5917763329, -1353304540200541571878546172822209767499349/455235779609983)
(12815508235932429635737/5041, -1189370763695611607988239287859020/357911)
(-832994856551886297743/441, 7845800097389037193736308804940/9261)
(133383363135166961560654286860288/110101349140561, 575116608676399937815060615947145466832918427118/1155284538322626187559)
(1415990583632388383053/121, 52749572836120173318259895698712/1331)
(1019134792912198389, -293004638496639875218600184)
(11396627246687935396278303859452862370722/9647120550614812677889, -429849001609041030909840248467392203879038277050788533425114/947537830606821820814341061763713)
(1260619969500769878475504279784725748381776/3157149436703306200809, 1415377646532396583520170537737729444528758887935306608264646518/177395544628415224275086681610123)
(3599588741587010043571/529, 209793704394355073944574283112742/12167)
(2014179191256997663402/3481, -144935521931240243298954228950485/205379)
(150032772058538652696448/241081, 76585317272244477727048810652889542/118370771)
(285917322645115051161114271389727105839437027578192/116706855383791196638038904729369, 3903145627145481058930209222461070638528301115917654279459614634325359889766/1260795212398509427268233177150991386097401798403)
(2220250364360615844829061802671722288/807814618233036241, 2790958517199962511713651508059547875407567959712703278/726051725465934318277048039)
(29161160018869290433/16, -106180930121531301695175958697/64)
(27159153367237303956978815922457/35788439734336, 100145923658062256110152198397537452082884053405/214098757714066563584)
(160352859850220798388223039347974287/107566198864416769, 34801750357984931737039871424405849395972440950989159/35278794203590116554139647)
(25476703351482383684326682581815685551697/639040795440876787984, -4062798172822279460514615479307576172402703902495103578699681/16154476008094858548425167564352)

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