↑

Properties

Label 22.6.221...064.1
Degree $22$
Signature $[6, 8]$
Discriminant $2.218\times 10^{121}$
Root discriminant \(327\,885.14\)
Ramified primes $2,1583,2731,6217$
Class number not computed
Class group not computed
Galois group $C_2^{10}.S_{11}$ (as 22T50)

Related objects

Downloads

Learn more

Show commands: Magma / Oscar / PariGP / SageMath

Normalized defining polynomial

sage: x = polygen(QQ); K.<a> = NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461)
 
gp: K = bnfinit(y^22 - 2092078224*y^20 + 2248666546255757077*y^18 - 1610791184294938633257411589*y^16 + 785414758509422230182481163809479264*y^14 - 276282651797678681220341949385050288006362704*y^12 + 72547298448676871921241338822312387845780976298859239*y^10 - 14704460207500777615949972454326335795506304085418908348229755*y^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*y^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*y^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*y^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461, 1)
 
magma: R<x> := PolynomialRing(Rationals()); K<a> := NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461);
 
oscar: Qx, x = PolynomialRing(QQ); K, a = NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461)
 

\( x^{22} - 2092078224 x^{20} + \cdots - 73\!\cdots\!61 \) Copy content Toggle raw display

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

Invariants

Degree:  $22$
sage: K.degree()
 
gp: poldegree(K.pol)
 
magma: Degree(K);
 
oscar: degree(K)
 
Signature:  $[6, 8]$
sage: K.signature()
 
gp: K.sign
 
magma: Signature(K);
 
oscar: signature(K)
 
Discriminant:   \(221\!\cdots\!064\) \(\medspace = 2^{22}\cdot 1583^{11}\cdot 2731^{11}\cdot 6217^{11}\) Copy content Toggle raw display
sage: K.disc()
 
gp: K.disc
 
magma: OK := Integers(K); Discriminant(OK);
 
oscar: OK = ring_of_integers(K); discriminant(OK)
 
Root discriminant:  \(327\,885.14\)
sage: (K.disc().abs())^(1./K.degree())
 
gp: abs(K.disc)^(1/poldegree(K.pol))
 
magma: Abs(Discriminant(OK))^(1/Degree(K));
 
oscar: (1.0 * dK)^(1/degree(K))
 
Galois root discriminant:  not computed
Ramified primes:   \(2\), \(1583\), \(2731\), \(6217\) Copy content Toggle raw display
sage: K.disc().support()
 
gp: factor(abs(K.disc))[,1]~
 
magma: PrimeDivisors(Discriminant(OK));
 
oscar: prime_divisors(discriminant((OK)))
 
Discriminant root field:  $\Q(\sqrt{26877166541}$)
$\card{ \Aut(K/\Q) }$:  $2$
sage: K.automorphisms()
 
magma: Automorphisms(K);
 
oscar: automorphisms(K)
 
This field is not Galois over $\Q$.
This is not a CM field.

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

$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $\frac{1}{26877166541}a^{6}-\frac{2092078224}{26877166541}a^{4}-\frac{8338228752}{26877166541}a^{2}$, $\frac{1}{26877166541}a^{7}-\frac{2092078224}{26877166541}a^{5}-\frac{8338228752}{26877166541}a^{3}$, $\frac{1}{72\!\cdots\!81}a^{8}-\frac{2092078224}{72\!\cdots\!81}a^{6}+\frac{22\!\cdots\!77}{72\!\cdots\!81}a^{4}+\frac{8153221724}{26877166541}a^{2}$, $\frac{1}{72\!\cdots\!81}a^{9}-\frac{2092078224}{72\!\cdots\!81}a^{7}+\frac{22\!\cdots\!77}{72\!\cdots\!81}a^{5}+\frac{8153221724}{26877166541}a^{3}$, $\frac{1}{19\!\cdots\!21}a^{10}-\frac{2092078224}{19\!\cdots\!21}a^{8}+\frac{22\!\cdots\!77}{19\!\cdots\!21}a^{6}-\frac{59\!\cdots\!29}{72\!\cdots\!81}a^{4}-\frac{5317133729}{26877166541}a^{2}$, $\frac{1}{19\!\cdots\!21}a^{11}-\frac{2092078224}{19\!\cdots\!21}a^{9}+\frac{22\!\cdots\!77}{19\!\cdots\!21}a^{7}-\frac{59\!\cdots\!29}{72\!\cdots\!81}a^{5}-\frac{5317133729}{26877166541}a^{3}$, $\frac{1}{52\!\cdots\!61}a^{12}-\frac{2092078224}{52\!\cdots\!61}a^{10}+\frac{22\!\cdots\!77}{52\!\cdots\!61}a^{8}-\frac{59\!\cdots\!29}{19\!\cdots\!21}a^{6}+\frac{10\!\cdots\!44}{72\!\cdots\!81}a^{4}-\frac{11922168435}{26877166541}a^{2}$, $\frac{1}{52\!\cdots\!61}a^{13}-\frac{2092078224}{52\!\cdots\!61}a^{11}+\frac{22\!\cdots\!77}{52\!\cdots\!61}a^{9}-\frac{59\!\cdots\!29}{19\!\cdots\!21}a^{7}+\frac{10\!\cdots\!44}{72\!\cdots\!81}a^{5}-\frac{11922168435}{26877166541}a^{3}$, $\frac{1}{14\!\cdots\!01}a^{14}-\frac{2092078224}{14\!\cdots\!01}a^{12}+\frac{22\!\cdots\!77}{14\!\cdots\!01}a^{10}-\frac{59\!\cdots\!29}{52\!\cdots\!61}a^{8}+\frac{10\!\cdots\!44}{19\!\cdots\!21}a^{6}-\frac{14229943268624}{72\!\cdots\!81}a^{4}+\frac{4637378294}{26877166541}a^{2}$, $\frac{1}{14\!\cdots\!01}a^{15}-\frac{2092078224}{14\!\cdots\!01}a^{13}+\frac{22\!\cdots\!77}{14\!\cdots\!01}a^{11}-\frac{59\!\cdots\!29}{52\!\cdots\!61}a^{9}+\frac{10\!\cdots\!44}{19\!\cdots\!21}a^{7}-\frac{14229943268624}{72\!\cdots\!81}a^{5}+\frac{4637378294}{26877166541}a^{3}$, $\frac{1}{75\!\cdots\!82}a^{16}+\frac{24785088317}{75\!\cdots\!82}a^{14}+\frac{33\!\cdots\!87}{37\!\cdots\!41}a^{12}-\frac{27\!\cdots\!18}{14\!\cdots\!01}a^{10}-\frac{72\!\cdots\!89}{10\!\cdots\!22}a^{8}+\frac{56\!\cdots\!75}{38\!\cdots\!42}a^{6}-\frac{11\!\cdots\!79}{72\!\cdots\!81}a^{4}-\frac{8243211560}{26877166541}a^{2}-\frac{1}{2}$, $\frac{1}{75\!\cdots\!82}a^{17}+\frac{24785088317}{75\!\cdots\!82}a^{15}+\frac{33\!\cdots\!87}{37\!\cdots\!41}a^{13}-\frac{27\!\cdots\!18}{14\!\cdots\!01}a^{11}-\frac{72\!\cdots\!89}{10\!\cdots\!22}a^{9}+\frac{56\!\cdots\!75}{38\!\cdots\!42}a^{7}-\frac{11\!\cdots\!79}{72\!\cdots\!81}a^{5}-\frac{8243211560}{26877166541}a^{3}-\frac{1}{2}a$, $\frac{1}{20\!\cdots\!62}a^{18}-\frac{1046039112}{10\!\cdots\!81}a^{16}+\frac{22\!\cdots\!77}{20\!\cdots\!62}a^{14}+\frac{36\!\cdots\!76}{37\!\cdots\!41}a^{12}+\frac{66\!\cdots\!41}{28\!\cdots\!02}a^{10}+\frac{33\!\cdots\!75}{52\!\cdots\!61}a^{8}-\frac{54\!\cdots\!37}{38\!\cdots\!42}a^{6}-\frac{36\!\cdots\!22}{72\!\cdots\!81}a^{4}+\frac{17799040095}{53754333082}a^{2}-\frac{1}{2}$, $\frac{1}{20\!\cdots\!62}a^{19}-\frac{1046039112}{10\!\cdots\!81}a^{17}+\frac{22\!\cdots\!77}{20\!\cdots\!62}a^{15}+\frac{36\!\cdots\!76}{37\!\cdots\!41}a^{13}+\frac{66\!\cdots\!41}{28\!\cdots\!02}a^{11}+\frac{33\!\cdots\!75}{52\!\cdots\!61}a^{9}-\frac{54\!\cdots\!37}{38\!\cdots\!42}a^{7}-\frac{36\!\cdots\!22}{72\!\cdots\!81}a^{5}+\frac{17799040095}{53754333082}a^{3}-\frac{1}{2}a$, $\frac{1}{19\!\cdots\!02}a^{20}+\frac{28\!\cdots\!89}{19\!\cdots\!02}a^{18}-\frac{58\!\cdots\!04}{99\!\cdots\!51}a^{16}+\frac{10\!\cdots\!19}{36\!\cdots\!11}a^{14}-\frac{19\!\cdots\!75}{27\!\cdots\!42}a^{12}-\frac{25\!\cdots\!43}{10\!\cdots\!62}a^{10}-\frac{31\!\cdots\!35}{19\!\cdots\!91}a^{8}+\frac{35\!\cdots\!89}{70\!\cdots\!51}a^{6}+\frac{24\!\cdots\!31}{52\!\cdots\!22}a^{4}-\frac{23\!\cdots\!83}{97\!\cdots\!71}a^{2}+\frac{20\!\cdots\!06}{36\!\cdots\!31}$, $\frac{1}{19\!\cdots\!02}a^{21}+\frac{28\!\cdots\!89}{19\!\cdots\!02}a^{19}-\frac{58\!\cdots\!04}{99\!\cdots\!51}a^{17}+\frac{10\!\cdots\!19}{36\!\cdots\!11}a^{15}-\frac{19\!\cdots\!75}{27\!\cdots\!42}a^{13}-\frac{25\!\cdots\!43}{10\!\cdots\!62}a^{11}-\frac{31\!\cdots\!35}{19\!\cdots\!91}a^{9}+\frac{35\!\cdots\!89}{70\!\cdots\!51}a^{7}+\frac{24\!\cdots\!31}{52\!\cdots\!22}a^{5}-\frac{23\!\cdots\!83}{97\!\cdots\!71}a^{3}+\frac{20\!\cdots\!06}{36\!\cdots\!31}a$ Copy content Toggle raw display

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

Monogenic:  Not computed
Index:  $1$
Inessential primes:  None

Class group and class number

not computed

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

Unit group

sage: UK = K.unit_group()
 
magma: UK, fUK := UnitGroup(K);
 
oscar: UK, fUK = unit_group(OK)
 
Rank:  $13$
sage: UK.rank()
 
gp: K.fu
 
magma: UnitRank(K);
 
oscar: rank(UK)
 
Torsion generator:   \( -1 \)  (order $2$) Copy content Toggle raw display
sage: UK.torsion_generator()
 
gp: K.tu[2]
 
magma: K!f(TU.1) where TU,f is TorsionUnitGroup(K);
 
oscar: torsion_units_generator(OK)
 
Fundamental units:  not computed
sage: UK.fundamental_units()
 
gp: K.fu
 
magma: [K|fUK(g): g in Generators(UK)];
 
oscar: [K(fUK(a)) for a in gens(UK)]
 
Regulator:  not computed
sage: K.regulator()
 
gp: K.reg
 
magma: Regulator(K);
 
oscar: regulator(K)
 

Class number formula

\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr $ not computed \end{aligned}\]

# self-contained SageMath code snippet to compute the analytic class number formula
 
x = polygen(QQ); K.<a> = NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461)
 
DK = K.disc(); r1,r2 = K.signature(); RK = K.regulator(); RR = RK.parent()
 
hK = K.class_number(); wK = K.unit_group().torsion_generator().order();
 
2^r1 * (2*RR(pi))^r2 * RK * hK / (wK * RR(sqrt(abs(DK))))
 
# self-contained Pari/GP code snippet to compute the analytic class number formula
 
K = bnfinit(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461, 1);
 
[polcoeff (lfunrootres (lfuncreate (K))[1][1][2], -1), 2^K.r1 * (2*Pi)^K.r2 * K.reg * K.no / (K.tu[1] * sqrt (abs (K.disc)))]
 
/* self-contained Magma code snippet to compute the analytic class number formula */
 
Qx<x> := PolynomialRing(QQ); K<a> := NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461);
 
OK := Integers(K); DK := Discriminant(OK);
 
UK, fUK := UnitGroup(OK); clK, fclK := ClassGroup(OK);
 
r1,r2 := Signature(K); RK := Regulator(K); RR := Parent(RK);
 
hK := #clK; wK := #TorsionSubgroup(UK);
 
2^r1 * (2*Pi(RR))^r2 * RK * hK / (wK * Sqrt(RR!Abs(DK)));
 
# self-contained Oscar code snippet to compute the analytic class number formula
 
Qx, x = PolynomialRing(QQ); K, a = NumberField(x^22 - 2092078224*x^20 + 2248666546255757077*x^18 - 1610791184294938633257411589*x^16 + 785414758509422230182481163809479264*x^14 - 276282651797678681220341949385050288006362704*x^12 + 72547298448676871921241338822312387845780976298859239*x^10 - 14704460207500777615949972454326335795506304085418908348229755*x^8 + 2998376416193315204664770130965065481838888904124682195000441934994554*x^6 - 306130763879319027589398803901949250419653698408383449814801242179261039446915*x^4 + 57185662090441204479231955581438591229270917896754221690045044001383130036100481435410*x^2 - 7318993160772087890271202123483045261112077972947622189086548235318321049181580865475206212461);
 
OK = ring_of_integers(K); DK = discriminant(OK);
 
UK, fUK = unit_group(OK); clK, fclK = class_group(OK);
 
r1,r2 = signature(K); RK = regulator(K); RR = parent(RK);
 
hK = order(clK); wK = torsion_units_order(K);
 
2^r1 * (2*pi)^r2 * RK * hK / (wK * sqrt(RR(abs(DK))))
 

Galois group

$C_2^{10}.S_{11}$ (as 22T50):

sage: K.galois_group(type='pari')
 
gp: polgalois(K.pol)
 
magma: G = GaloisGroup(K);
 
oscar: G, Gtx = galois_group(K); G, transitive_group_identification(G)
 
A non-solvable group of order 40874803200
The 376 conjugacy class representatives for $C_2^{10}.S_{11}$
Character table for $C_2^{10}.S_{11}$

Intermediate fields

11.3.26877166541.1

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

sage: K.subfields()[1:-1]
 
gp: L = nfsubfields(K); L[2..length(b)]
 
magma: L := Subfields(K); L[2..#L];
 
oscar: subfields(K)[2:end-1]
 

Sibling fields

Degree 22 sibling: data not computed
Degree 44 sibling: data not computed
Minimal sibling: This field is its own minimal sibling

Frobenius cycle types

$p$ $2$ $3$ $5$ $7$ $11$ $13$ $17$ $19$ $23$ $29$ $31$ $37$ $41$ $43$ $47$ $53$ $59$
Cycle type R ${\href{/padicField/3.14.0.1}{14} }{,}\,{\href{/padicField/3.4.0.1}{4} }^{2}$ ${\href{/padicField/5.12.0.1}{12} }{,}\,{\href{/padicField/5.4.0.1}{4} }{,}\,{\href{/padicField/5.3.0.1}{3} }^{2}$ ${\href{/padicField/7.10.0.1}{10} }{,}\,{\href{/padicField/7.6.0.1}{6} }{,}\,{\href{/padicField/7.3.0.1}{3} }^{2}$ ${\href{/padicField/11.11.0.1}{11} }^{2}$ ${\href{/padicField/13.6.0.1}{6} }^{2}{,}\,{\href{/padicField/13.3.0.1}{3} }^{2}{,}\,{\href{/padicField/13.2.0.1}{2} }^{2}$ ${\href{/padicField/17.11.0.1}{11} }^{2}$ ${\href{/padicField/19.10.0.1}{10} }{,}\,{\href{/padicField/19.6.0.1}{6} }^{2}$ ${\href{/padicField/23.9.0.1}{9} }^{2}{,}\,{\href{/padicField/23.4.0.1}{4} }$ ${\href{/padicField/29.14.0.1}{14} }{,}\,{\href{/padicField/29.6.0.1}{6} }{,}\,{\href{/padicField/29.1.0.1}{1} }^{2}$ ${\href{/padicField/31.11.0.1}{11} }^{2}$ ${\href{/padicField/37.8.0.1}{8} }{,}\,{\href{/padicField/37.7.0.1}{7} }^{2}$ ${\href{/padicField/41.8.0.1}{8} }^{2}{,}\,{\href{/padicField/41.2.0.1}{2} }^{3}$ $20{,}\,{\href{/padicField/43.1.0.1}{1} }^{2}$ ${\href{/padicField/47.10.0.1}{10} }^{2}{,}\,{\href{/padicField/47.1.0.1}{1} }^{2}$ ${\href{/padicField/53.12.0.1}{12} }{,}\,{\href{/padicField/53.8.0.1}{8} }{,}\,{\href{/padicField/53.1.0.1}{1} }^{2}$ ${\href{/padicField/59.5.0.1}{5} }^{2}{,}\,{\href{/padicField/59.4.0.1}{4} }^{2}{,}\,{\href{/padicField/59.2.0.1}{2} }^{2}$

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

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

Local algebras for ramified primes

$p$LabelPolynomial $e$ $f$ $c$ Galois group Slope content
\(2\) Copy content Toggle raw display 2.10.10.9$x^{10} + 10 x^{9} + 22 x^{8} - 8 x^{7} + 72 x^{6} + 1328 x^{5} + 4496 x^{4} + 3680 x^{3} - 3696 x^{2} - 96 x - 32$$2$$5$$10$$C_2 \times (C_2^4 : C_5)$$[2, 2, 2, 2, 2]^{5}$
2.12.12.1$x^{12} + 16 x^{11} + 100 x^{10} + 184 x^{9} + 44 x^{8} - 1472 x^{7} - 2336 x^{6} - 1600 x^{5} + 18032 x^{4} + 37504 x^{3} + 66880 x^{2} + 40064 x + 13120$$2$$6$$12$12T134$[2, 2, 2, 2, 2, 2]^{6}$
\(1583\) Copy content Toggle raw display Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $4$$2$$2$$2$
Deg $4$$2$$2$$2$
Deg $12$$2$$6$$6$
\(2731\) Copy content Toggle raw display Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $4$$2$$2$$2$
Deg $12$$2$$6$$6$
\(6217\) Copy content Toggle raw display Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $2$$2$$1$$1$$C_2$$[\ ]_{2}$
Deg $4$$2$$2$$2$
Deg $14$$2$$7$$7$