curve #693

y² = x³ + x² − 2061017599086828493684524369017988453336167414331726430380x + 36878430076454023011583051989238273786308751689793868971418268804247600351950004774128

a-invariants: [0, 1, 0, -2061017599086828493684524369017988453336167414331726430380, 36878430076454023011583051989238273786308751689793868971418268804247600351950004774128]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 250279241610432014044436972659843895088719817403294274822780582989744217318747851038398671958158215758891968187619511122924709552440
discriminant (Δ): -27222293257870344537757254472747086600161935095166781240098353103238166607153736950937466465059592589069764003043823608054898681382278589315763447169723674393512737100000000
Faltings height: 31.8675
naive height: 407.5727
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 31, 41, 43, 71, 193, 199, 101560519, 463388207737677317, 909300088216110792923085910267, 372641792931529883394767954213873931728546577952271624747
regulator: 5302761750029582252531643151502244.06668676478335834206721853760665541890575499996535211556263874
submitted by: wgxli
submitted at: 2026-09-10 14:27:47 UTC
last updated: 2026-09-10 14:27:47 UTC

Witness: 29 independent points log in to add more points →

(20051411727182107475482009176748763769513376495172014480999866/1148555145579316257330857772151441, 97063876805005097211504992962777120246529806262556401120221195737812003955742278786522007650/38924924396901241741474929952423497908925003890489)
(1708603717196081189350674395241/16, -2058526677011887817052306380245306788335532675/64)
(1184321094205910435580873674346/25, -843686604955570242029087611076348933772920694/125)
(2614563689242380810059334631269/100, 929957739249369636878002579282912639650688047/1000)
(718555091588023488682908171715133481789727266414/34660864318334665489, 357024972806864027750644427073761835580359270081275374006907086232345550/204060563879880785942089387513)
(38835540445341442146239225688, 3925484536347111459027438164946998001498948)
(1127031034321991699526359096148834/2809, 37603760099355559954951539993871261613711230526850/148877)
(463229866374476673794330900472917192399713825807546/22706230607268298370721, -6236650493103290334982032662224164289277065776165062263934991351354414233650/3421508052419797760467222093401231)
(531794544487488297229892001698581175458247185717374264/12588290160440835798810889, 224222940941564567662963604100931341351669218708843064098063866385876076915061500/44663228937886371931124428169762423963)
(77050883480020488692142293208426/2401, -228942359084237989502482536204667630510278961950/117649)
(37881282348766313936616712761145443025127972346/3016002929101104721, 18865685913309346530992376361792022817368575529320412550202384066158750/5237784648841351879634312231)
(283038152140921290979404608608947012216384174429/8936148151564804, -150579906958440440616217888088786159933957149813109695390541558737705875/844744826017499103014408)
(-23143989773358572338174858617, -8495978753267942423247089040027092595819858)
(-79482768360450460323970750651880711708034/5314311267841, 98281591327145290665705958944170779456792573422290679027863250/12250970165217232639)
(541893187942245589018354915550001/15376, 5398097338316564484751731791005231362051718076625/1906624)
(6051827769207592079583467064388061686932504/52901285648929, -13863605846617108286817514274911302085305480742946813177866227300/384768349245067816783)
(1339400735380821412542509824564081438157200344/46458057609763969, -11941149140158133569077744161896283016606752730618784523844156613500/10013630736638167498351297)
(159526937149394827376705139604790141066635416/147668736642163801, -334044488566854449955753490682863401381503148806918230126803092803380/56745684491435851382660701)
(61380698470639193776021879529542486456/182007081, -476748288628580688261058296321251382184941275527453701500/2455457529771)
(2713490519243240486926598728649892606717/3841272484, 141064114207981275355354075442036528651572007850732880186029/238074386013352)
(381057609555809698774329013901198795334144551706/1778533659885664081, -230335944706610260278730240600315390803553650531343395020622846443178750/2371882295269127642265933479)
(92410832839097694884205065880965877798/2959686409, 277301836942212027606673010816725996859846546077274539230/161015819708827)
(1068494811841770927402211327341808837361/69822736, 34926632757719221156915671988369990054993386208675563344625/583438782016)
(5168287089661367723160184904181326112832901334/94402840868705209, -272301917792207394465293738295029744436548123912768180478841154681250/29005315621396588988709677)
(9452242294755317007815224663007753470773431543974/109834879344390681849, -25658490813133892734406217685782827715275225662204170768129489259573687250/1151093008011774397476965904243)
(15813663344632458797908090521082387784086/483677129961, 709027318920800941607683369817131853508227454375897239896750/336382449896846709)
(6291084248169682579513303335264018119779322396577171/36841499243146759762225, -482941252786866318139984491600639045193493931416633226974780059612895031568956/7071408770962935504945499324220375)
(1235004774335733332839285618979732671496669181/6034125538373956, -42415783016851584818157233684736415409428344761209001923570381668675/468728663330941857212104)
(41492482028167648851739374545286540867892350051/1471448086236694801, -1941362269585897642195100102305172914185561597828080085985809130674000/1784914496341274023626817799)

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