curve #1838

y² + xy + y = x³ − 59213416100392645484638647882713527227270080470823x + 175477375755633227633843793733607188300929975425820078326280356331740037278

a-invariants

[1, 0, 1, -59213416100392645484638647882713527227270080470823, 175477375755633227633843793733607188300929975425820078326280356331740037278]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

749953252894866358381288818682207333534845733376227936415913300112172540779754947678427922992593607302039871479600222770

discriminant (Δ)

-14868012088010434882640297158507539589780738303688675150271614247946231422617958361770400816157353970084093791099149744212522184972009481160411062500

Faltings height

27.3718

naive height

355.4304

primes of bad reduction

2, 3, 5, 11, 13, 23, 29, 31, 37, 43, 103, 113, 193, 81703, 374111, 25060703453442814696743129263491, 3088264417475034741258296824081468228143908756270188175954239

regulator

41234205134778855228984600275622.76157956986547238922583805100062964456531056967020232225689064

submitted by

Ritik Jain

submitted at

2026-09-25 16:44:16 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:16:42 UTC

Witness: 28 independent points log in to add more points →

(-3482974335264455774297091, 18424544466059115234972103864458706870)
(81359163110569071754418060825785230771372111952514943793323552062871/18736873130999583483102332086670473564356169, 39046193077044524530200771690204603018756874764316984198480546153854471540806726087466225494299526410/81104635014223875819734579923568442440458524817204991239993055803)
(44561603054642026482856869/16, 362973658676828781744284784404165164855/64)
(53425562530138553664537600714/5041, -9725259946161220411104018103015022086824445/357911)
(213644844928876581831781041/49, -148927455727041012173520325882080443540/343)
(4531946129569853858234609, 452660259057743437743708417012752820)
(6061611235289295472420929, -6266677087849906411346351483054100620)
(4405636888565414038743288, 341138646777139309269521028493276258)
(94452222248483224483239687276/4489, -27309351871237752175783999463671888323467990/300763)
(3913308940216773150702609, -1919725721290323647324944697695391180)
(551808634542792809278387989/121, 709673474820340683984542386502464709570/1331)
(4437859684508454416597709, -313701609352858376593352523061898330)
(12145901937619491483452045151/289, -1317560759000198329658269410944250589494190/4913)
(4824988396462390787060109, -1449667330966687973996597861269880180)
(-2834648662211218210073923596/361, 85747913993594694551391917189437767662215/6859)
(284806179033146522958676401/64, -160948868754199411225056063581764067635/512)
(660372977005537955487952562318398911/123887808529, 146582532473949154771982742907041476924024878950962810/43605659182611833)
(4174484881516686185999024615284191421278756994117986/946123967292021210238327609, 9673347505022365581805201651262177641135184372837886681616096082584659855535/29101948397921656191364833007174219694227)
(18645208875404784300606313660469447324226/3227006504722009, 938979547178505379547815848944941136861200310965044092936680/183315742081097470594723)
(-8790428360566878821200565903428601442127956628805981065800520691257416835105500077739/4048107893377077084700113644500369358794408490082170399253904, 139610579399420239690042427947524019569505611691572748785327458666718588594020213594844716071597001875970379907515715030910718215/8144756758455002642041651787858300428446372614029372332946972608284575913715941199640745792)
(1104791617748720695997967059390665902059606694496615031901617047000246626712986734099405319/97042326582128140241148512284402689170911180888431415737006894841, 944866567985054965910843664539389431283605602657573923104400624238060076529751615030407844631621145925406678255140549248382858836936330/30230254280233422540219035002400537124222965019035345010649649674358098974903429631874874496257139)
(460067050503251554004284521987374728754904/106286014303898881, 18014226021189643106282635612130846117925631732007089465996030/34650873109964728788913279)
(3143330657695540257125928000797571193149/753177033053041, 21131516449532579516174080986572246415379961441116957807850/20670243970677003969911)
(2454739428640625620210760237814510174913186873851900503578/597463020732080392765440472533609, 18173995936461170528206746666084180546023981419554131222699603763741270941496482606336/14603822490595724948615513364016818044814090478773)
(1215696935687095742978301872512823527809031588701/273477799328062554910864, 44812771374951700773554724208048458134398547969934753439076636452009835/143015501952590646035213163383789888)
(-429665447068631571549521799059064005902280932833416397846509056485370136234611848556236629760892397487322403494701189896640370729606/155895568379917533891070673738048447966561561140782923781796826798349889289848472984120059270616892351083761, 1097202518764208992039689579911280069882036818448618713585521997768010030476962067949173085577838868690275698712699699582049464744211465463234533234805356574644626804715013319664705392876989730094480/61553202671614932695170363916888840902703146021547062907361171967163627732067404711044495273830252903470693608089355605155724501399699791465983121340197042119991)
(4645573739201454520337858448095568859548556727939673358429260692327905031157648/481496110478900690507699054418865526475291660798491449, 7488123786225280587778125117298189875550255707893764138615206962340772478152153617846887524613632803670577638955553694/334109769583117127374656131027308889132737917630249094248738922680559061232578707)
(4063078508001044165907414701032407694940808942317010083093560668128060361/3154162239250949662617500301140286514172075413504, 56391401059927914979713988792410557160846996237109656954800652620641835543357459661798250154207223104638604965/5601779917404512661371879418467430976164699265212070955165044358314196992)

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