curve #1983

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y² + xy + y = x³ − 19366673285537451391760631367686815276x + 31395075406030702292629746432584979680972612225855873798

a-invariants: [1, 0, 1, -19366673285537451391760631367686815276, 31395075406030702292629746432584979680972612225855873798]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 486330793397648792679267826394094393499487256148655133709585232511904931223434985535350
discriminant (Δ): 39083356729136399056685677613071558896664429694783112132126293353239110309145269234726047093701744214169242792500
Faltings height: 20.3641
naive height: 269.1835
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 41, 53, 83, 945181065189767412394133697576354388807267182282989408749942389875519397589
regulator: 1082440833444389619168618.5279776637858215899291119684818805068223131136630367241584383
submitted by: Ritik Jain
submitted at: 2026-09-25 23:06:00 UTC
last updated: 2026-09-25 23:06:00 UTC

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

(4722913960028000909196542871472704731120516672763/1362537733346783377044680399689, 3867196077664391499056068458119171720271753928353310598895568303756319797/1590460205948977767812976821950081048895155387)
(51279353870705412429/25, -68532877158929421658966092643/125)
(19745326087635053098371/5041, 1415106025790861352032613065062937/357911)
(69756556965885298981/81, -2856652774837712580957351889751/729)
(7453456722619509027, 17352690754557757821314827021)
(8566427337401426412, -22228985935070847444188978534)
(17028624307959904098983/289, -2216094014175013167495842900116617/4913)
(3820723675797045289969947/303601, 7059239177378539608320586686359980761/167284151)
(-1756899988734205021347/361, 22095298810271041979145784404163/6859)
(-6697014870746086104267/2209, 819110712739642855080211747794143/103823)
(154360631781213720717, -1917035290718310078859875437819)
(-1523218279575501369, -7573677069658450768173327599)
(-9133886905737681651227/33489, -37104893547995360587250608450499993/6128487)
(3015940280613289767, 647320477451688311636879281)
(-9958465482075555741/25, -781088617884868117525288115533/125)
(-129424439955242262684305479317/151689217729, -406306190256725879691135152109561420656956283/59078854696566817)
(-1072565570421449230661694237/2696621041, 874898603785783451364351243924852795043463/140032834038089)
(4316095783159162117484569195076785899/2831989086909675625, 11094468736706145409820463584491156809889727684255350943/4765817012089850817302796875)
(2089433344651359341168429810545464737685561996418334142/1216177417493814194708467751838101929, 2396783254107716020190979371538145170364511586411656848961144694282561320854895002/1341205737073459044316297622487018073315021945287138283)
(-1309239580867875634987364527457217644504346633/303844402292038314051483121, 31262792076455195183770020249279167182975212290045913814526812025401/5296352227996711386020469741195043627081)
(68901349739189128658827220391412542873544839599/35371411636902003539251494289, 6853482814494099274322607494215973008282854748869405766598248535691471/6652403580211563138508175827954824409070663)
(-1580632769496987703622912414948085497718370628648955417/504260964456457519462743276038949169, 2803642152939250183138667480907498431009003992785517962875995375378667056726053143/358082440830023847259399713854212777160702488386617303)
(-6301856042717535172715876399567884971678920097/39461221939561643227209971329, 46032378990933240372311218010187663398306539487001737805581139508225337/7838912088309239730026439710789873205384767)
(-14701217721345760429769181646937599882770600427489707/4571661589738096144882661860803049, 2402700555200912429779504319421104135020966859974519779370788736377537368099977/309108617257465047961680523385102729797629203943157)

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