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Properties

Label 36.0.27685721416...2944.1
Degree $36$
Signature $[0, 18]$
Discriminant $2^{36}\cdot 3^{18}\cdot 7^{24}\cdot 13^{24}$
Root discriminant $70.08$
Ramified primes $2, 3, 7, 13$
Class number $3888$ (GRH)
Class group $[3, 6, 6, 6, 6]$ (GRH)
Galois group $C_6^2$ (as 36T4)

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Show commands for: Magma / SageMath / Pari/GP

magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R![4096, 0, -263168, 0, 15590144, 0, -79576832, 0, 257155248, 0, -519473400, 0, 764272865, 0, -785267530, 0, 597601939, 0, -315209926, 0, 124149567, 0, -36148410, 0, 8063896, 0, -1343558, 0, 169571, 0, -15244, 0, 994, 0, -40, 0, 1]);
 
sage: x = polygen(QQ); K.<a> = NumberField(x^36 - 40*x^34 + 994*x^32 - 15244*x^30 + 169571*x^28 - 1343558*x^26 + 8063896*x^24 - 36148410*x^22 + 124149567*x^20 - 315209926*x^18 + 597601939*x^16 - 785267530*x^14 + 764272865*x^12 - 519473400*x^10 + 257155248*x^8 - 79576832*x^6 + 15590144*x^4 - 263168*x^2 + 4096)
 
gp: K = bnfinit(x^36 - 40*x^34 + 994*x^32 - 15244*x^30 + 169571*x^28 - 1343558*x^26 + 8063896*x^24 - 36148410*x^22 + 124149567*x^20 - 315209926*x^18 + 597601939*x^16 - 785267530*x^14 + 764272865*x^12 - 519473400*x^10 + 257155248*x^8 - 79576832*x^6 + 15590144*x^4 - 263168*x^2 + 4096, 1)
 

Normalized defining polynomial

\( x^{36} - 40 x^{34} + 994 x^{32} - 15244 x^{30} + 169571 x^{28} - 1343558 x^{26} + 8063896 x^{24} - 36148410 x^{22} + 124149567 x^{20} - 315209926 x^{18} + 597601939 x^{16} - 785267530 x^{14} + 764272865 x^{12} - 519473400 x^{10} + 257155248 x^{8} - 79576832 x^{6} + 15590144 x^{4} - 263168 x^{2} + 4096 \)

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:  \(2768572141683771661071455896880577445777843907315454304309104082944=2^{36}\cdot 3^{18}\cdot 7^{24}\cdot 13^{24}\)
magma: Discriminant(Integers(K));
 
sage: K.disc()
 
gp: K.disc
 
Root discriminant:  $70.08$
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:  $2, 3, 7, 13$
magma: PrimeDivisors(Discriminant(Integers(K)));
 
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
This field is Galois and abelian over $\Q$.
Conductor:  \(1092=2^{2}\cdot 3\cdot 7\cdot 13\)
Dirichlet character group:    $\lbrace$$\chi_{1092}(1,·)$, $\chi_{1092}(107,·)$, $\chi_{1092}(263,·)$, $\chi_{1092}(653,·)$, $\chi_{1092}(911,·)$, $\chi_{1092}(529,·)$, $\chi_{1092}(659,·)$, $\chi_{1092}(919,·)$, $\chi_{1092}(29,·)$, $\chi_{1092}(289,·)$, $\chi_{1092}(547,·)$, $\chi_{1092}(295,·)$, $\chi_{1092}(809,·)$, $\chi_{1092}(1075,·)$, $\chi_{1092}(625,·)$, $\chi_{1092}(53,·)$, $\chi_{1092}(443,·)$, $\chi_{1092}(445,·)$, $\chi_{1092}(575,·)$, $\chi_{1092}(835,·)$, $\chi_{1092}(373,·)$, $\chi_{1092}(841,·)$, $\chi_{1092}(79,·)$, $\chi_{1092}(781,·)$, $\chi_{1092}(211,·)$, $\chi_{1092}(599,·)$, $\chi_{1092}(347,·)$, $\chi_{1092}(989,·)$, $\chi_{1092}(991,·)$, $\chi_{1092}(737,·)$, $\chi_{1092}(235,·)$, $\chi_{1092}(365,·)$, $\chi_{1092}(113,·)$, $\chi_{1092}(757,·)$, $\chi_{1092}(191,·)$, $\chi_{1092}(893,·)$$\rbrace$
This is a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $a^{12}$, $\frac{1}{2} a^{13} - \frac{1}{2} a^{9} - \frac{1}{2} a^{5} - \frac{1}{2} a^{3} - \frac{1}{2} a$, $\frac{1}{4} a^{14} - \frac{1}{2} a^{12} - \frac{1}{4} a^{10} - \frac{1}{4} a^{6} - \frac{1}{4} a^{4} + \frac{1}{4} a^{2}$, $\frac{1}{4} a^{15} - \frac{1}{4} a^{11} - \frac{1}{2} a^{9} - \frac{1}{4} a^{7} + \frac{1}{4} a^{5} - \frac{1}{4} a^{3} - \frac{1}{2} a$, $\frac{1}{12} a^{16} + \frac{1}{4} a^{12} - \frac{1}{6} a^{10} - \frac{1}{12} a^{8} - \frac{1}{4} a^{6} - \frac{5}{12} a^{4} - \frac{1}{6} a^{2} + \frac{1}{3}$, $\frac{1}{12} a^{17} - \frac{1}{4} a^{13} - \frac{1}{6} a^{11} + \frac{5}{12} a^{9} - \frac{1}{4} a^{7} + \frac{1}{12} a^{5} + \frac{1}{3} a^{3} - \frac{1}{6} a$, $\frac{1}{12} a^{18} + \frac{1}{3} a^{12} + \frac{1}{6} a^{10} - \frac{1}{4} a^{8} - \frac{1}{6} a^{6} + \frac{1}{12} a^{4} + \frac{1}{12} a^{2}$, $\frac{1}{12} a^{19} - \frac{1}{6} a^{13} + \frac{1}{6} a^{11} + \frac{1}{4} a^{9} - \frac{1}{6} a^{7} - \frac{5}{12} a^{5} - \frac{5}{12} a^{3} - \frac{1}{2} a$, $\frac{1}{12} a^{20} + \frac{1}{12} a^{14} - \frac{1}{3} a^{12} - \frac{1}{6} a^{8} + \frac{1}{3} a^{6} + \frac{1}{3} a^{4} - \frac{1}{4} a^{2}$, $\frac{1}{12} a^{21} + \frac{1}{12} a^{15} + \frac{1}{6} a^{13} + \frac{1}{3} a^{9} + \frac{1}{3} a^{7} - \frac{1}{6} a^{5} + \frac{1}{4} a^{3} - \frac{1}{2} a$, $\frac{1}{12} a^{22} - \frac{1}{12} a^{14} + \frac{1}{4} a^{12} - \frac{1}{4} a^{10} + \frac{5}{12} a^{8} + \frac{1}{3} a^{6} - \frac{1}{12} a^{4} + \frac{5}{12} a^{2} - \frac{1}{3}$, $\frac{1}{12} a^{23} - \frac{1}{12} a^{15} - \frac{1}{4} a^{13} - \frac{1}{4} a^{11} - \frac{1}{12} a^{9} + \frac{1}{3} a^{7} + \frac{5}{12} a^{5} - \frac{1}{12} a^{3} + \frac{1}{6} a$, $\frac{1}{36} a^{24} + \frac{1}{6} a^{12} + \frac{1}{6} a^{10} - \frac{1}{4} a^{8} + \frac{11}{36} a^{6} + \frac{1}{12} a^{4} + \frac{1}{12} a^{2} - \frac{2}{9}$, $\frac{1}{36} a^{25} + \frac{1}{6} a^{13} + \frac{1}{6} a^{11} - \frac{1}{4} a^{9} + \frac{11}{36} a^{7} + \frac{1}{12} a^{5} + \frac{1}{12} a^{3} - \frac{2}{9} a$, $\frac{1}{36} a^{26} - \frac{1}{12} a^{14} - \frac{1}{3} a^{12} + \frac{11}{36} a^{8} + \frac{1}{3} a^{6} + \frac{1}{3} a^{4} - \frac{17}{36} a^{2}$, $\frac{1}{72} a^{27} - \frac{1}{24} a^{19} + \frac{1}{12} a^{15} - \frac{1}{12} a^{13} + \frac{7}{24} a^{11} + \frac{5}{18} a^{9} - \frac{3}{8} a^{7} - \frac{1}{2} a^{5} + \frac{25}{72} a^{3}$, $\frac{1}{144} a^{28} - \frac{1}{72} a^{24} + \frac{1}{48} a^{20} - \frac{1}{24} a^{18} - \frac{1}{8} a^{14} - \frac{7}{48} a^{12} - \frac{23}{72} a^{10} + \frac{1}{48} a^{8} - \frac{29}{72} a^{6} - \frac{59}{144} a^{4} - \frac{1}{4} a^{2} + \frac{4}{9}$, $\frac{1}{288} a^{29} + \frac{1}{144} a^{25} - \frac{1}{24} a^{23} + \frac{1}{96} a^{21} - \frac{1}{48} a^{19} + \frac{5}{48} a^{15} + \frac{13}{96} a^{13} + \frac{61}{144} a^{11} + \frac{17}{96} a^{9} + \frac{23}{144} a^{7} - \frac{71}{288} a^{5} - \frac{1}{6} a^{3} - \frac{2}{9} a$, $\frac{1}{5264064} a^{30} - \frac{1411}{658008} a^{28} + \frac{17369}{2632032} a^{26} + \frac{15869}{1316016} a^{24} + \frac{15163}{584896} a^{22} - \frac{11787}{292448} a^{20} + \frac{293}{219336} a^{18} + \frac{17089}{877344} a^{16} - \frac{205163}{1754688} a^{14} - \frac{785363}{2632032} a^{12} + \frac{762227}{5264064} a^{10} + \frac{1223491}{2632032} a^{8} + \frac{1605809}{5264064} a^{6} - \frac{16693}{658008} a^{4} + \frac{106531}{329004} a^{2} + \frac{23906}{82251}$, $\frac{1}{10528128} a^{31} - \frac{1411}{1316016} a^{29} + \frac{17369}{5264064} a^{27} + \frac{15869}{2632032} a^{25} - \frac{100735}{3509376} a^{23} + \frac{37751}{1754688} a^{21} - \frac{5995}{146224} a^{19} + \frac{17089}{1754688} a^{17} + \frac{29095}{1169792} a^{15} - \frac{566027}{5264064} a^{13} - \frac{4063165}{10528128} a^{11} - \frac{2285885}{5264064} a^{9} - \frac{2780911}{10528128} a^{7} - \frac{455365}{1316016} a^{5} - \frac{70111}{329004} a^{3} + \frac{51323}{164502} a$, $\frac{1}{319807743360768} a^{32} + \frac{654617}{26650645280064} a^{30} - \frac{5818829}{5922365617792} a^{28} + \frac{572567306711}{79951935840192} a^{26} + \frac{89714448703}{24600595643136} a^{24} - \frac{1112928719}{214061407872} a^{22} + \frac{2114025541}{256256204616} a^{20} - \frac{1270702872623}{53301290560128} a^{18} + \frac{1761568685245}{106602581120256} a^{16} - \frac{11922599743949}{159903871680384} a^{14} - \frac{5264405163703}{106602581120256} a^{12} - \frac{18086124441517}{53301290560128} a^{10} - \frac{34099696281319}{319807743360768} a^{8} - \frac{2568499464073}{79951935840192} a^{6} + \frac{3158589296623}{6662661320016} a^{4} - \frac{81125905465}{262999788948} a^{2} + \frac{250449644074}{1249248997503}$, $\frac{1}{639615486721536} a^{33} + \frac{654617}{53301290560128} a^{31} - \frac{5818829}{11844731235584} a^{29} + \frac{572567306711}{159903871680384} a^{27} - \frac{593635430273}{49201191286272} a^{25} + \frac{5575173979}{142707605248} a^{23} - \frac{19240658177}{512512409232} a^{21} - \frac{1270702872623}{106602581120256} a^{19} + \frac{1761568685245}{213205162240512} a^{17} - \frac{38573245024013}{319807743360768} a^{15} + \frac{39153336969737}{213205162240512} a^{13} - \frac{40294995508237}{106602581120256} a^{11} + \frac{232406756519321}{639615486721536} a^{9} + \frac{52953678202727}{159903871680384} a^{7} - \frac{172741363385}{13325322640032} a^{5} - \frac{47677287715}{131499894474} a^{3} - \frac{568802398798}{1249248997503} a$, $\frac{1}{3780659482697685817797569101666408593951349978862592} a^{34} + \frac{249190846975338882554456728702145471}{945164870674421454449392275416602148487837494715648} a^{32} + \frac{18434302822249655236712599137630627864145337}{210036637927649212099864950092578255219519443270144} a^{30} + \frac{497191577227582946075324044247422435699018769279}{945164870674421454449392275416602148487837494715648} a^{28} + \frac{22831278127889556830565669299906493458148899681}{198982078036720306199872057982442557576386840992768} a^{26} + \frac{14834755771028004607218546558924934437123048375571}{1890329741348842908898784550833204296975674989431296} a^{24} + \frac{140911580434704009240476975460254003279293838105}{4922733701429278408590584767794802856707486951644} a^{22} - \frac{1288090948377769378588836220574466980747354630839}{70012212642549737366621650030859418406506481090048} a^{20} + \frac{45169501966310998208955585958842850275928167073757}{1260219827565895272599189700555469531317116659620864} a^{18} - \frac{3496829474311500675388100484728860583848919220887}{99491039018360153099936028991221278788193420496384} a^{16} + \frac{311438836032866407766227644274894960750873645881211}{3780659482697685817797569101666408593951349978862592} a^{14} - \frac{19906273496898014622024402153716383423634112236087}{210036637927649212099864950092578255219519443270144} a^{12} + \frac{821480611545561535765496366332303089772465374106937}{3780659482697685817797569101666408593951349978862592} a^{10} + \frac{11590394273359093288341194663817988751453565390253}{24234996683959524473061340395297490986867628069632} a^{8} + \frac{78428576913030952060795032721575087250213787075377}{236291217668605363612348068854150537121959373678912} a^{6} + \frac{2660827950946829459985515041813481328613162677097}{29536402208575670451543508606768817140244921709864} a^{4} + \frac{2600490877226714901822526071646918413636367}{10693582565156133176860058697602237577150498} a^{2} + \frac{1263207781928923343289262322923384315272452836049}{3692050276071958806442938575846102142530615213733}$, $\frac{1}{7561318965395371635595138203332817187902699957725184} a^{35} + \frac{249190846975338882554456728702145471}{1890329741348842908898784550833204296975674989431296} a^{33} + \frac{18434302822249655236712599137630627864145337}{420073275855298424199729900185156510439038886540288} a^{31} + \frac{497191577227582946075324044247422435699018769279}{1890329741348842908898784550833204296975674989431296} a^{29} + \frac{22831278127889556830565669299906493458148899681}{397964156073440612399744115964885115152773681985536} a^{27} - \frac{37674403710884298417747690964219629367756812441965}{3780659482697685817797569101666408593951349978862592} a^{25} + \frac{140911580434704009240476975460254003279293838105}{9845467402858556817181169535589605713414973903288} a^{23} - \frac{1288090948377769378588836220574466980747354630839}{140024425285099474733243300061718836813012962180096} a^{21} - \frac{59848816997513607840976889087446277333831554561315}{2520439655131790545198379401110939062634233319241728} a^{19} - \frac{3496829474311500675388100484728860583848919220887}{198982078036720306199872057982442557576386840992768} a^{17} - \frac{633726034641555046683164631141707187736963848834437}{7561318965395371635595138203332817187902699957725184} a^{15} - \frac{19906273496898014622024402153716383423634112236087}{420073275855298424199729900185156510439038886540288} a^{13} + \frac{506425654654087717615698941193435706943186209201721}{7561318965395371635595138203332817187902699957725184} a^{11} - \frac{527104068620668948189475533830756741980248644563}{48469993367919048946122680790594981973735256139264} a^{9} - \frac{131608061014618260039069917371003167969305656194767}{472582435337210727224696137708301074243918747357824} a^{7} + \frac{5122194801661468664280807425710882756966906152919}{59072804417151340903087017213537634280489843419728} a^{5} - \frac{3710337049843347843738330104708027820352681}{42774330260624532707440234790408950308601992} a^{3} - \frac{804193438619077864194289395811792008903457276205}{3692050276071958806442938575846102142530615213733} a$

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

Class group and class number

$C_{3}\times C_{6}\times C_{6}\times C_{6}\times C_{6}$, which has order $3888$ (assuming GRH)

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:  \( -\frac{6060142282926036761565678419595515159142905}{3481270241894738322097209117556545666621869225472} a^{35} + \frac{2102427275536353136901628816355733513776637}{30537458262234546685063237873303032163349730048} a^{33} - \frac{2958206200830205367148893464527528366924468851}{1740635120947369161048604558778272833310934612736} a^{31} + \frac{5608687881313688732268570363957255908029901047}{217579390118421145131075569847284104163866826592} a^{29} - \frac{329257009464956993229100773065785101964712401081}{1160423413964912774032403039185515222207289741824} a^{27} + \frac{1926471090036884730879263531838262948012089742595}{870317560473684580524302279389136416655467306368} a^{25} - \frac{315923993362214035715072675478961415416631985507}{24175487790935682792341729983031567129318536288} a^{23} + \frac{33221042796812807101072354703310375552697634496931}{580211706982456387016201519592757611103644870912} a^{21} - \frac{222354101988818733977029445601701016644443050262537}{1160423413964912774032403039185515222207289741824} a^{19} + \frac{407396320282967231915837883332995172909091880241615}{870317560473684580524302279389136416655467306368} a^{17} - \frac{11864529695950455726572697388311702515505820227547}{13981004987529069566655458303439942436232406528} a^{15} + \frac{34535989601497481895928736015261086516055031172079}{33473752325910945404780856899582169871364127168} a^{13} - \frac{367162940785913993455269197211529249993969168503409}{386807804654970924677467679728505074069096580608} a^{11} + \frac{8978483581844683474221383654239490894083644555023}{15681397486012334784221662691696151651449861376} a^{9} - \frac{75226743502499184660099803282936792739683145288371}{290105853491228193508100759796378805551822435456} a^{7} + \frac{5007808412584996193597752554707156845083686486801}{108789695059210572565537784923642052081933413296} a^{5} - \frac{194048518255739209098079272240306726228607}{249451281446244972818098361270033780191356} a^{3} - \frac{52131653302030731807773507873867566528024864259}{6799355941200660785346111557727628255120838331} a \) (order $12$)
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
sage: UK.torsion_generator()
 
gp: K.tu[2]
 
Fundamental units:  Units are too long to display, but can be downloaded with other data for this field from 'Stored data to gp' link to the right (assuming GRH)
magma: [K!f(g): g in Generators(UK)];
 
sage: UK.fundamental_units()
 
gp: K.fu
 
Regulator:  \( 7748254634341177.0 \) (assuming GRH)
magma: Regulator(K);
 
sage: K.regulator()
 
gp: K.reg
 

Galois group

$C_6^2$ (as 36T4):

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 $C_6^2$
Character table for $C_6^2$ is not computed

Intermediate fields

\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{3}) \), \(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})^+\), 3.3.169.1, 3.3.8281.2, 3.3.8281.1, \(\Q(\zeta_{12})\), 6.0.64827.1, 6.0.771147.1, 6.0.1851523947.1, 6.0.1851523947.2, 6.6.4148928.1, 6.0.153664.1, 6.6.49353408.1, 6.0.1827904.1, 6.6.118497532608.2, 6.0.4388797504.1, 6.6.118497532608.3, 6.0.4388797504.2, 9.9.567869252041.1, 12.0.17213603549184.1, 12.0.2435758881214464.1, 12.0.14041665234184023281664.1, 12.0.14041665234184023281664.2, 18.0.6347285018761982937208599123.3, 18.18.1663902683958341255091611008499712.1, 18.0.84535014172552012147112280064.1

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 R R ${\href{/LocalNumberField/5.6.0.1}{6} }^{6}$ R ${\href{/LocalNumberField/11.6.0.1}{6} }^{6}$ R ${\href{/LocalNumberField/17.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/19.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/23.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/29.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/31.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/37.3.0.1}{3} }^{12}$ ${\href{/LocalNumberField/41.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/43.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/47.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/53.6.0.1}{6} }^{6}$ ${\href{/LocalNumberField/59.6.0.1}{6} }^{6}$

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
$2$2.12.12.26$x^{12} - 162 x^{10} + 26423 x^{8} + 125508 x^{6} - 64481 x^{4} - 122498 x^{2} - 86071$$2$$6$$12$$C_6\times C_2$$[2]^{6}$
2.12.12.26$x^{12} - 162 x^{10} + 26423 x^{8} + 125508 x^{6} - 64481 x^{4} - 122498 x^{2} - 86071$$2$$6$$12$$C_6\times C_2$$[2]^{6}$
2.12.12.26$x^{12} - 162 x^{10} + 26423 x^{8} + 125508 x^{6} - 64481 x^{4} - 122498 x^{2} - 86071$$2$$6$$12$$C_6\times C_2$$[2]^{6}$
$3$3.12.6.2$x^{12} + 108 x^{6} - 243 x^{2} + 2916$$2$$6$$6$$C_6\times C_2$$[\ ]_{2}^{6}$
3.12.6.2$x^{12} + 108 x^{6} - 243 x^{2} + 2916$$2$$6$$6$$C_6\times C_2$$[\ ]_{2}^{6}$
3.12.6.2$x^{12} + 108 x^{6} - 243 x^{2} + 2916$$2$$6$$6$$C_6\times C_2$$[\ ]_{2}^{6}$
7Data not computed
$13$13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$
13.3.2.2$x^{3} - 13$$3$$1$$2$$C_3$$[\ ]_{3}$