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Properties

Label 36.0.97651534536...3125.1
Degree $36$
Signature $[0, 18]$
Discriminant $3^{54}\cdot 5^{27}\cdot 7^{30}$
Root discriminant $87.93$
Ramified primes $3, 5, 7$
Class number Not computed
Class group Not computed
Galois group $C_3\times C_{12}$ (as 36T3)

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Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![1759249171, 187966461, 3957820605, 1219028741, 5636834421, 2918077776, 5853643895, 3581139363, 5006204397, 2916789821, 3580401840, 1740513231, 1993614817, 857521695, 821493693, 364897592, 246367347, 122149350, 55944685, 27824757, 11476701, 3598192, 2244003, 80127, 219791, -69369, -40545, -17223, -12486, -2232, -151, -153, 261, -4, 30, 0, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^36 + 30*x^34 - 4*x^33 + 261*x^32 - 153*x^31 - 151*x^30 - 2232*x^29 - 12486*x^28 - 17223*x^27 - 40545*x^26 - 69369*x^25 + 219791*x^24 + 80127*x^23 + 2244003*x^22 + 3598192*x^21 + 11476701*x^20 + 27824757*x^19 + 55944685*x^18 + 122149350*x^17 + 246367347*x^16 + 364897592*x^15 + 821493693*x^14 + 857521695*x^13 + 1993614817*x^12 + 1740513231*x^11 + 3580401840*x^10 + 2916789821*x^9 + 5006204397*x^8 + 3581139363*x^7 + 5853643895*x^6 + 2918077776*x^5 + 5636834421*x^4 + 1219028741*x^3 + 3957820605*x^2 + 187966461*x + 1759249171)
 
gp: K = bnfinit(x^36 + 30*x^34 - 4*x^33 + 261*x^32 - 153*x^31 - 151*x^30 - 2232*x^29 - 12486*x^28 - 17223*x^27 - 40545*x^26 - 69369*x^25 + 219791*x^24 + 80127*x^23 + 2244003*x^22 + 3598192*x^21 + 11476701*x^20 + 27824757*x^19 + 55944685*x^18 + 122149350*x^17 + 246367347*x^16 + 364897592*x^15 + 821493693*x^14 + 857521695*x^13 + 1993614817*x^12 + 1740513231*x^11 + 3580401840*x^10 + 2916789821*x^9 + 5006204397*x^8 + 3581139363*x^7 + 5853643895*x^6 + 2918077776*x^5 + 5636834421*x^4 + 1219028741*x^3 + 3957820605*x^2 + 187966461*x + 1759249171, 1)
 

Normalized defining polynomial

\( x^{36} + 30 x^{34} - 4 x^{33} + 261 x^{32} - 153 x^{31} - 151 x^{30} - 2232 x^{29} - 12486 x^{28} - 17223 x^{27} - 40545 x^{26} - 69369 x^{25} + 219791 x^{24} + 80127 x^{23} + 2244003 x^{22} + 3598192 x^{21} + 11476701 x^{20} + 27824757 x^{19} + 55944685 x^{18} + 122149350 x^{17} + 246367347 x^{16} + 364897592 x^{15} + 821493693 x^{14} + 857521695 x^{13} + 1993614817 x^{12} + 1740513231 x^{11} + 3580401840 x^{10} + 2916789821 x^{9} + 5006204397 x^{8} + 3581139363 x^{7} + 5853643895 x^{6} + 2918077776 x^{5} + 5636834421 x^{4} + 1219028741 x^{3} + 3957820605 x^{2} + 187966461 x + 1759249171 \)

magma: DefiningPolynomial(K);
 
sage: K.defining_polynomial()
 
gp: K.pol
 

Invariants

Degree:  $36$
magma: Degree(K);
 
sage: K.degree()
 
gp: poldegree(K.pol)
 
Signature:  $[0, 18]$
magma: Signature(K);
 
sage: K.signature()
 
gp: K.sign
 
Discriminant:  \(9765153453691149470292712667475504049384715601795025169849395751953125=3^{54}\cdot 5^{27}\cdot 7^{30}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $87.93$
magma: Abs(Discriminant(Integers(K)))^(1/Degree(K));
 
sage: (K.disc().abs())^(1./K.degree())
 
gp: abs(K.disc)^(1/poldegree(K.pol))
 
Ramified primes:  $3, 5, 7$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(315=3^{2}\cdot 5\cdot 7\)
Dirichlet character group:    $\lbrace$$\chi_{315}(256,·)$, $\chi_{315}(1,·)$, $\chi_{315}(4,·)$, $\chi_{315}(257,·)$, $\chi_{315}(143,·)$, $\chi_{315}(16,·)$, $\chi_{315}(17,·)$, $\chi_{315}(274,·)$, $\chi_{315}(278,·)$, $\chi_{315}(151,·)$, $\chi_{315}(152,·)$, $\chi_{315}(289,·)$, $\chi_{315}(293,·)$, $\chi_{315}(38,·)$, $\chi_{315}(167,·)$, $\chi_{315}(169,·)$, $\chi_{315}(173,·)$, $\chi_{315}(46,·)$, $\chi_{315}(47,·)$, $\chi_{315}(184,·)$, $\chi_{315}(188,·)$, $\chi_{315}(62,·)$, $\chi_{315}(64,·)$, $\chi_{315}(68,·)$, $\chi_{315}(79,·)$, $\chi_{315}(83,·)$, $\chi_{315}(214,·)$, $\chi_{315}(272,·)$, $\chi_{315}(226,·)$, $\chi_{315}(227,·)$, $\chi_{315}(106,·)$, $\chi_{315}(109,·)$, $\chi_{315}(211,·)$, $\chi_{315}(248,·)$, $\chi_{315}(121,·)$, $\chi_{315}(122,·)$$\rbrace$
This is a CM field.

Integral basis (with respect to field generator \(a\))

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $a^{13}$, $a^{14}$, $a^{15}$, $a^{16}$, $a^{17}$, $a^{18}$, $a^{19}$, $a^{20}$, $a^{21}$, $a^{22}$, $a^{23}$, $a^{24}$, $a^{25}$, $a^{26}$, $a^{27}$, $a^{28}$, $a^{29}$, $a^{30}$, $a^{31}$, $a^{32}$, $\frac{1}{295891} a^{33} + \frac{109}{449} a^{32} - \frac{26215}{295891} a^{31} - \frac{138517}{295891} a^{30} + \frac{146100}{295891} a^{29} - \frac{21390}{295891} a^{28} - \frac{85062}{295891} a^{27} - \frac{93665}{295891} a^{26} + \frac{34611}{295891} a^{25} - \frac{110579}{295891} a^{24} + \frac{10919}{295891} a^{23} + \frac{50694}{295891} a^{22} - \frac{26269}{295891} a^{21} + \frac{13869}{295891} a^{20} + \frac{7374}{295891} a^{19} + \frac{35803}{295891} a^{18} - \frac{11505}{295891} a^{17} - \frac{46635}{295891} a^{16} + \frac{61351}{295891} a^{15} + \frac{48012}{295891} a^{14} - \frac{72013}{295891} a^{13} - \frac{131420}{295891} a^{12} + \frac{111461}{295891} a^{11} + \frac{139157}{295891} a^{10} + \frac{10508}{295891} a^{9} - \frac{142977}{295891} a^{8} - \frac{4101}{295891} a^{7} + \frac{99484}{295891} a^{6} - \frac{125358}{295891} a^{5} + \frac{31926}{295891} a^{4} + \frac{23569}{295891} a^{3} + \frac{118648}{295891} a^{2} - \frac{25491}{295891} a - \frac{147740}{295891}$, $\frac{1}{83811700968356472721} a^{34} + \frac{4509562126898}{83811700968356472721} a^{33} + \frac{37589228880975576272}{83811700968356472721} a^{32} - \frac{8841501747652323350}{83811700968356472721} a^{31} + \frac{33577833326660841451}{83811700968356472721} a^{30} - \frac{3672962169948007322}{83811700968356472721} a^{29} - \frac{9032332556577871240}{83811700968356472721} a^{28} + \frac{29673805993308101281}{83811700968356472721} a^{27} - \frac{34157982600292741640}{83811700968356472721} a^{26} - \frac{32435279745784970951}{83811700968356472721} a^{25} - \frac{4443874451894551085}{83811700968356472721} a^{24} - \frac{40005671136067254171}{83811700968356472721} a^{23} + \frac{14668170069912510188}{83811700968356472721} a^{22} - \frac{32754516320203855208}{83811700968356472721} a^{21} + \frac{35839475916790078544}{83811700968356472721} a^{20} - \frac{31548826991807664331}{83811700968356472721} a^{19} + \frac{13502133900162648710}{83811700968356472721} a^{18} + \frac{25686043443981196931}{83811700968356472721} a^{17} - \frac{22363113932545019516}{83811700968356472721} a^{16} - \frac{8813325285273006402}{83811700968356472721} a^{15} + \frac{31457989340336414025}{83811700968356472721} a^{14} - \frac{30216316512938654704}{83811700968356472721} a^{13} - \frac{7276561424460158132}{83811700968356472721} a^{12} + \frac{28948250249065946953}{83811700968356472721} a^{11} - \frac{35275683695432217400}{83811700968356472721} a^{10} - \frac{28250158750302446164}{83811700968356472721} a^{9} + \frac{4781024523978968946}{83811700968356472721} a^{8} - \frac{3674755241329079185}{83811700968356472721} a^{7} + \frac{32819124253058402100}{83811700968356472721} a^{6} + \frac{38888767039215122931}{83811700968356472721} a^{5} - \frac{41830947145696561910}{83811700968356472721} a^{4} - \frac{32981725378118254881}{83811700968356472721} a^{3} - \frac{10189605158975869757}{83811700968356472721} a^{2} + \frac{26324929247330601151}{83811700968356472721} a + \frac{28442024505064419352}{83811700968356472721}$, $\frac{1}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{35} + \frac{956387911481711679812759423511465929470593161610013667606125703870732609132181369975202884067653328697261464849872021789967893677000737321}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{34} + \frac{225007365284706707903657244835477210729102067789724908675706402745536522396705116491321445764394358920619893271007944023288220062576986091604800878368129}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{33} + \frac{83982772628816201052848448747194576453220552880328084703119306907339508932782869846341497756675052351159073851253269913524790564978193354250121867087714457892}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{32} + \frac{81302102472689402931595809452473162127886767461633091958087452797474272202975976122195073922726638763074671640572802742261177089573516172011717188626914473670}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{31} - \frac{108224751562317983329694142344725739690937678784275883321953941941227690953191646074900494147246537478035998707662074831855757055574520931636305562388119958299}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{30} + \frac{105570251373168761382497669187836024577209961394617688783740353637747806708390679399397061935578976592939301231016678129473627847470280458981400733826080252763}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{29} + \frac{70906031413605738453537748280579370819588266335483197343181379098139549876134828721961425568865351875184177329233180054759426613525549175409771213378064108422}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{28} + \frac{100912539062091895873932808023594446907820538814368950470362912222019368076334408534095085481320052547761172546457375655067697398906670600157564869940232362800}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{27} + \frac{154409752039249023321463673218661715508821853008508506857232319083763222439992511868866937132547032486918356066608435074364145977910825597603108825152116758679}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{26} - \frac{62084833702908042496868832168204613245566643994271970071695747951564635476620327118106802085304936232607473762246923788973804357507334997209762879338256228800}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{25} - \frac{145577464743612733050812158928043514452075512257424970520165465220375025152944062925061856423353424615976539508485760665314205719972455968648344836266692850175}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{24} - \frac{50715636020010199996254439890660731589225933826034314216540860395090097813401568187691429523779895193496895590630897685837574491663038273336964036131793056968}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{23} + \frac{87185865075891320289336875301554586452249489834715886314550888771426837381859130684251455058603824340415412899952789378084028060944727405593905846681057063903}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{22} + \frac{84322845948794285722516143013180062783255077875085807252629682365256530635111918846518414421715721144708806459118287793684838850814976002290924264977327620609}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{21} - \frac{53145491157170170196430911715512357187551915240908842932094399251805392892566437330846174379287148815455069314236082279168800132081147943766110805599697555334}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{20} + \frac{88670327862060403507441390674926251349614957075687076210290468790139764880586113106926288672606913826807733840432530993205253338347473477786639692275278032514}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{19} + \frac{121140325167303386140100931556643028522230186625505543667602408011944049102977613089548223105593468879551935261173521842876965882257805925663534405983144364743}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{18} + \frac{139580656164217363218354244371201847378508619853389716874341324252681776265845009033662899256885830801372215345794977236162608241304575990773209016170123100194}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{17} - \frac{126826706747808730135166002567773977206363192953335907882257188454150879741778193933364978347338046303104654009283525890506033064692049170938508768755012780777}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{16} + \frac{64869644287202613837686438265156496994587938098034892259308947486596674656850177775963260240699105185600231819249472960350342444370629611309109036304713384846}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{15} - \frac{138985452217616478552237532398081180027360196627152540416385213485983827690033629295367959343608227537006323610316913480766189155892835575357837019443820461342}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{14} + \frac{2334392452838429595888790402427454404598158047088968671710507765463998402616924349953583690510751250033604620426265645514566372268309012081342020713173928801}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{13} + \frac{63760084166078134289067940188052101004414166562182926008868130152351917380456949268816686365916300957959119457342780082494883412165736385369438938937161277245}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{12} - \frac{92767886286983732991176175177359251976607595513700570818878424293641497525312030878900023490405864180309339928491211412989822221035619356913489533064920589735}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{11} - \frac{163460961967990038385917149649031648661244021016384218381170793525921999294078466459795308903657859933848751167610858541815537360102347885923233699667605662675}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{10} - \frac{2940640828190904273397498317915770107291482625009919037316354055211995795946464215929962733838828114895595855203096093289286928146601365673787260785725324185}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{9} - \frac{65496622724591623093270942355046146153708613084011104751986479565971040211501531693509947908145405747550826710942860823311123894479334919183137752355367427436}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{8} + \frac{119955309821077238049430891162333795251572126233205652634882693497181306794079651683416302044288381806900694471919962872098301538452758265013840722909005401796}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{7} + \frac{72575574198348150512336393713297019621638777741027762632471164028593080889983550762110169999205248771746306415606218362052599066607985066649132083347353940198}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{6} + \frac{145351722298687721284419164330716108759066691418438970383642693113458753210240714352080236018350412677217697149627102235807644567815168581359582452105975366484}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{5} + \frac{19109875825777373350932006223770383679916164870063536442356544768889443289840940876392651908570888043430888200897224553561878214217407597833409201080465278626}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{4} + \frac{62658377553287592208295578774304631592884677423506374822039027938915175230088138083639058016497817379713669351616724909515474737528322685945243386863779656107}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{3} + \frac{85129019385400496139138923191961481126634961513484568065325422724437253504343328723966120699182340108611124147397391328776274880913722662362628097611989774503}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a^{2} + \frac{142387668707283754921013514910947205517049540995710989385160987670761222731146271873576219840255919910866152198134265822235226314996641422604316505022094027460}{328552669524880739169395199212727091961204304141568738858194051250631724203526131944636009979346653103833311522341487008780628661051850487977811498820700742451} a - \frac{80184926353269566239934498746834107610204404185504702997647202950947373991176411515401599421129487863847585758050066892773996166054805601795025335831}{186757325193521855676574423812945535252552524375507429958137550971528480659733749531854126409786810752934162685668525467095774269403848130605605667681}$

magma: IntegralBasis(K);
 
sage: K.integral_basis()
 
gp: K.zk
 

Class group and class number

Not computed

magma: ClassGroup(K);
 
sage: K.class_group().invariants()
 
gp: K.clgp
 

Unit group

magma: UK, f := UnitGroup(K);
 
sage: UK = K.unit_group()
 
Rank:  $17$
magma: UnitRank(K);
 
sage: UK.rank()
 
gp: K.fu
 
Torsion generator:  \( -1 \) (order $2$)
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
sage: UK.torsion_generator()
 
gp: K.tu[2]
 
Fundamental units:  Not computed
magma: [K!f(g): g in Generators(UK)];
 
sage: UK.fundamental_units()
 
gp: K.fu
 
Regulator:  Not computed
magma: Regulator(K);
 
sage: K.regulator()
 
gp: K.reg
 

Galois group

$C_3\times C_{12}$ (as 36T3):

magma: GaloisGroup(K);
 
sage: K.galois_group(type='pari')
 
gp: polgalois(K.pol)
 
An abelian group of order 36
The 36 conjugacy class representatives for $C_3\times C_{12}$
Character table for $C_3\times C_{12}$ is not computed

Intermediate fields

\(\Q(\sqrt{5}) \), \(\Q(\zeta_{9})^+\), 3.3.3969.1, \(\Q(\zeta_{7})^+\), 3.3.3969.2, 4.0.55125.1, 6.6.820125.1, 6.6.1969120125.1, 6.6.300125.1, 6.6.1969120125.2, 9.9.62523502209.1, 12.0.89022720918673828125.1, 12.0.213743552925735861328125.2, 12.0.402196204142578125.1, 12.0.213743552925735861328125.1, 18.18.7635133454060210702501953125.1

Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.

Frobenius cycle types

$p$ 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Cycle type ${\href{/LocalNumberField/2.12.0.1}{12} }^{3}$ R R R ${\href{/LocalNumberField/11.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/13.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/17.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/19.3.0.1}{3} }^{12}$ ${\href{/LocalNumberField/23.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/29.3.0.1}{3} }^{12}$ ${\href{/LocalNumberField/31.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/37.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/41.3.0.1}{3} }^{12}$ ${\href{/LocalNumberField/43.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/47.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/53.12.0.1}{12} }^{3}$ ${\href{/LocalNumberField/59.6.0.1}{6} }^{6}$

In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.

magma: p := 7; // to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
magma: idealfactors := Factorization(p*Integers(K)); // get the data
 
magma: [<primefactor[2], Valuation(Norm(primefactor[1]), p)> : primefactor in idealfactors];
 
sage: p = 7; # to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
sage: [(e, pr.norm().valuation(p)) for pr,e in K.factor(p)]
 
gp: p = 7; \\ to obtain a list of $[e_i,f_i]$ for the factorization of the ideal $p\mathcal{O}_K$:
 
gp: idealfactors = idealprimedec(K, p); \\ get the data
 
gp: vector(length(idealfactors), j, [idealfactors[j][3], idealfactors[j][4]])
 

Local algebras for ramified primes

$p$LabelPolynomial $e$ $f$ $c$ Galois group Slope content
3Data not computed
$5$5.12.9.2$x^{12} - 10 x^{8} + 25 x^{4} - 500$$4$$3$$9$$C_{12}$$[\ ]_{4}^{3}$
5.12.9.2$x^{12} - 10 x^{8} + 25 x^{4} - 500$$4$$3$$9$$C_{12}$$[\ ]_{4}^{3}$
5.12.9.2$x^{12} - 10 x^{8} + 25 x^{4} - 500$$4$$3$$9$$C_{12}$$[\ ]_{4}^{3}$
7Data not computed