curve #443

y² + xy + y = x³ − 470205160918761195421530423911518748067291843154934193054292446585122015228136823x + 3790838284044638260603760507410155823669268918149579764831861050275267231873985142865201191329587809161081790942820131278

a-invariants: [1, 0, 1, -470205160918761195421530423911518748067291843154934193054292446585122015228136823, 3790838284044638260603760507410155823669268918149579764831861050275267231873985142865201191329587809161081790942820131278]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 56993902717135009670510089927275630828232412232399997224714957481273143775768712246228587944644276266701364816257552730143642559182488778170246821379443523032250701765218617464043115250749211442382476819283016660274271224790
discriminant (Δ): 445340732883664790714293908319584338932763381801410571986224274132632455507280034916973172350714717398965749860708252336979397414363123377245431984402489335120535749407983138479963339112142399035455458097723374482264826862344424813469380937500
Faltings height: 45.3275
naive height: 568.8780
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 41, 20753, 4823245517, 1229541702511273638317, 2336145096738873840251488875701801405383763350597471678069873803239412118461355706452747520417877758453728003943051216055757249277412456897253151814610790312635576624376801294008829
regulator: 75324379596502301555606975365.33456260662139091867152853932771247554668133880
submitted by: Nikita-Shulga
submitted at: 2026-08-30 14:03:53 UTC
last updated: 2026-09-02 17:34:59 UTC

Witness: 19 independent points log in to add more points →

(-19564823347712187614698448768082650818641, -2345474550581009743609350169700879759152522025140422544483430)
(-16385293510711946277165685962608767486736, 2663869289246539165638979931347246039622300239789667950912085)
(3158933970234596079495874269116110051468981/9, -5604018410137280164935217999375765446271680998058545165784146860/27)
(-3454855441555737539086019466618265383380454/169, 4843293401004729772246148978185144619620216688221096437318410665/2197)
(136586684686978846181651879105673834842101/9, 10466461475366459807303821848558412788489933089789176547292850/27)
(8960676942579501702768406906093206683389, 544947636692082674638230550382678934986181672034933220294150)
(20106128513733349619987232208300058671759, 1569988566299196120198884331751273155570813774209038633245770)
(-334941103661546508869023881772663414794323/16, 135164452242154026263964178662652318550879275302283239963404993/64)
(4440130742733960417172425069052009453006384, -9355962402447880822486012051529302285588349890243710954218161030)
(-193781642039910772395184945006833990734451/16, 177697780082449692309585630656849387556980272334069983344642715/64)
(46408685560870504674221001713462128410319, -9051115308017136472926719154628949666990440455702275440595770)
(61909830020230219619307732131488788887749, 14559195996118141630489824160774198769908466205554858717345660)
(6624777351757277222887940488911481334489869/16, 17028334070603501449420503564081239827441583083409567342844413105/64)
(29158916634923531142624363717986783765338, 3856463797315077100580618094362372499963174516936342860568773)
(-11098362889279191799461356617215935205761, -2764474602582687633564589999437185583767962390210059090897490)
(15465768519477715030778142353642019587089, 466916713500010300590374604869721569226987211968911866844810)
(7288519790118584941221094091675677915609, 866558253622264699636419293590048649701710544708824420046820)
(-78520595833841806745949068622170793337967/64, -1069807901932850078631421124024179304449806456707861520040831331/512)
(120950459658151423616145258444833891927655559/2601, -1204717094513968948251089946775236682565001073277799320766401884130/132651)

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