curve #1986

← home · all curves · JSON ↓

y² = x³ − 200608373971748575008008441996236355457x + 1102766839214730800031036889295937188670708484727512531881

a-invariants

[0, 0, 0, -200608373971748575008008441996236355457, 1102766839214730800031036889295937188670708484727512531881]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

3031130899217664228662184373284396564503249340839092866798699563411550830926174718170999507652746860

discriminant (Δ)

-8666372042841282238096837174178122717709003123167106092541804123922667242326347855612069247305836187009961139750000

Faltings height

20.8747

naive height

276.2135

primes of bad reduction

2, 3, 5, 13, 23, 29, 41, 47, 690712858344585214187122057, 30268938254466219740125971467, 48204386217547088174237733225908149

regulator

1325273022609498526264867386.201732862106982522912999398008409810654600658284221098432949

submitted by

Ritik Jain

submitted at

2026-09-25 23:06:10 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:12 UTC

Witness: 25 independent points log in to add more points →

(9875003385920603235008005368791982616750643613/759063097911469803646443649, 551232101019786531446410353915026257917013954995188307299472579210825/20913023133674130467995676796520250419393)
(-27507531145954975976703/11881, 51064480681391244765608451911409975/1295029)
(21270160317030043944288/49, -3100471691872108264249253926421925/343)
(9528592743530089737, -7509404198389248167857161525)
(8732273908135111562165885733945/538751596009, -18161689897487911226365772688924724245722994303/395442055215817973)
(351373538109709041639/25, 4069053245056512343803443087463/125)
(11178521520820620201, 16035040469036652585314109525)
(12655044568099691658513/1369, -313301715317470558439921769990705/50653)
(5926814021306971437, -11044919612441721685085739225)
(7849579319932927377, -3425544420385208366170013085)
(392307280600453037847, -7765336799410999173997556188485)
(3287800025115625437, -21880276980573962293515681975)
(1695372662265962187, -27704401748578939444291521225)
(35734089058716080673/4, 38857607708670553871972834775/8)
(58129179070766295987, 431115005145674224834988100975)
(84100087687431442045227537/8561476, 224107330639715329671726152940864759375/25050878776)
(2519883959245664613807/361, -44753649518176867533079893350025/6859)
(2550364312976953727179128370786722367/1615543390840397841, 57715816819946749789026867969195094759599974540538920075/2053420722230385316295637639)
(2068300797019637648581933494930460332384496191248810250480/396926687788207243036034832888025324009, 111534474981110788127541241786252442195519041486023004443980048978838404859885185360217/7907977959484016565773903028071835672907483600601552364277)
(374978837870582869491483608313/132254414224, 1134896087389462388381410356100328605579315725/48096698312013632)
(314654511025246457322124540922204973345/34573829301315063841, 1129084830042899773215530813357201826085222842858661348419/203292438458370411866346860111)
(-942100603319679137551391930247995279211028413/57914985710034195419005081, 3458974281209513978594690765398238429282351988226450576519750153515/440744021790384620218384928984615943229)
(437997107497425095222216893602851556410369762679737878600530614488/55574702310290851276632711008108436672354473329, 43961029281807299728203610521249382341112327347679671135247673147432122062157773996940792027156655/13101340005249317536783938120924118671062286401466058157641962827364983)
(-117238362047080448560001341728085795074847044402651156109466314809831/14099746979983459213882199386419927179839341184144, 2480998789953805963006068299432495840710860843502979125965340456789055833928809619625008784523434976515/52944027934976080055434260863324447617213303599786228180526593963949313728)
(67369584207569852006764564993650366854893492318803272074424575776039498246298031282839195033/12272124693541894430631951345861277838786894978480767486626092152769230369, 555461281159365678039330900137900690595400296428774280242303076373566956582015152723862792522138229807899738259471511966670522987269430315/42991207071968084263830110073316383488150996954097514657669859647463303945782752530625684469248708068863853903)

Commentary

No commentary yet.