Normalized defining polynomial
\( x^{22} - 11 x^{21} - 15789084607 x^{20} + 157890846455 x^{19} + \cdots - 20\!\cdots\!71 \)
Invariants
Degree: | $22$ | sage: K.degree()
gp: poldegree(K.pol)
magma: Degree(K);
oscar: degree(K)
| |
Signature: | $[18, 2]$ | sage: K.signature()
gp: K.sign
magma: Signature(K);
oscar: signature(K)
| |
Discriminant: | \(651\!\cdots\!449\) \(\medspace = 29^{10}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681^{10}\) | sage: K.disc()
gp: K.disc
magma: OK := Integers(K); Discriminant(OK);
oscar: OK = ring_of_integers(K); discriminant(OK)
| |
Root discriminant: | \(1\,088\,890.74\) | 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: | $29^{1/2}151^{1/2}2311^{1/2}24910163^{1/2}1702694681^{1/2}\approx 655155090331.9882$ | ||
Ramified primes: | \(29\), \(151\), \(2311\), \(24910163\), \(1702694681\) | sage: K.disc().support()
gp: factor(abs(K.disc))[,1]~
magma: PrimeDivisors(Discriminant(OK));
oscar: prime_divisors(discriminant((OK)))
| |
Discriminant root field: | \(\Q\) | ||
$\card{ \Aut(K/\Q) }$: | $2$ | 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 \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $\frac{1}{49378145749}a^{4}-\frac{2}{49378145749}a^{3}-\frac{3444548226}{49378145749}a^{2}+\frac{3444548227}{49378145749}a-\frac{22464075822}{49378145749}$, $\frac{1}{49378145749}a^{5}-\frac{3444548230}{49378145749}a^{3}-\frac{118777525}{1702694681}a^{2}-\frac{15574979368}{49378145749}a+\frac{4449994105}{49378145749}$, $\frac{1}{24\!\cdots\!01}a^{6}-\frac{3}{24\!\cdots\!01}a^{5}-\frac{15789084661}{24\!\cdots\!01}a^{4}+\frac{31578169327}{24\!\cdots\!01}a^{3}-\frac{49\!\cdots\!12}{24\!\cdots\!01}a^{2}+\frac{49\!\cdots\!48}{24\!\cdots\!01}a+\frac{75\!\cdots\!08}{24\!\cdots\!01}$, $\frac{1}{24\!\cdots\!01}a^{7}-\frac{15789084670}{24\!\cdots\!01}a^{5}-\frac{15789084656}{24\!\cdots\!01}a^{4}-\frac{49\!\cdots\!31}{24\!\cdots\!01}a^{3}-\frac{99\!\cdots\!88}{24\!\cdots\!01}a^{2}-\frac{19\!\cdots\!49}{24\!\cdots\!01}a-\frac{18\!\cdots\!77}{24\!\cdots\!01}$, $\frac{1}{12\!\cdots\!49}a^{8}-\frac{4}{12\!\cdots\!49}a^{7}+\frac{21244524654}{12\!\cdots\!49}a^{6}-\frac{63733573948}{12\!\cdots\!49}a^{5}-\frac{10\!\cdots\!71}{12\!\cdots\!49}a^{4}+\frac{21\!\cdots\!84}{12\!\cdots\!49}a^{3}+\frac{20\!\cdots\!74}{12\!\cdots\!49}a^{2}-\frac{20\!\cdots\!90}{12\!\cdots\!49}a-\frac{22\!\cdots\!89}{12\!\cdots\!49}$, $\frac{1}{12\!\cdots\!49}a^{9}+\frac{21244524638}{12\!\cdots\!49}a^{7}+\frac{21244524668}{12\!\cdots\!49}a^{6}-\frac{10\!\cdots\!63}{12\!\cdots\!49}a^{5}+\frac{27\!\cdots\!01}{12\!\cdots\!49}a^{4}+\frac{20\!\cdots\!08}{12\!\cdots\!49}a^{3}+\frac{53\!\cdots\!80}{12\!\cdots\!49}a^{2}+\frac{23\!\cdots\!27}{12\!\cdots\!49}a-\frac{24\!\cdots\!29}{12\!\cdots\!49}$, $\frac{1}{59\!\cdots\!01}a^{10}-\frac{5}{59\!\cdots\!01}a^{9}+\frac{8899988221}{59\!\cdots\!01}a^{8}-\frac{35599952854}{59\!\cdots\!01}a^{7}+\frac{10\!\cdots\!80}{59\!\cdots\!01}a^{6}-\frac{32\!\cdots\!72}{59\!\cdots\!01}a^{5}-\frac{43\!\cdots\!44}{59\!\cdots\!01}a^{4}+\frac{86\!\cdots\!55}{59\!\cdots\!01}a^{3}+\frac{97\!\cdots\!26}{59\!\cdots\!01}a^{2}-\frac{97\!\cdots\!08}{59\!\cdots\!01}a-\frac{17\!\cdots\!56}{59\!\cdots\!01}$, $\frac{1}{59\!\cdots\!01}a^{11}+\frac{8899988196}{59\!\cdots\!01}a^{9}+\frac{8899988251}{59\!\cdots\!01}a^{8}+\frac{10\!\cdots\!10}{59\!\cdots\!01}a^{7}-\frac{25\!\cdots\!73}{59\!\cdots\!01}a^{6}-\frac{43\!\cdots\!01}{59\!\cdots\!01}a^{5}+\frac{25\!\cdots\!96}{59\!\cdots\!01}a^{4}+\frac{97\!\cdots\!74}{59\!\cdots\!01}a^{3}-\frac{83\!\cdots\!67}{59\!\cdots\!01}a^{2}-\frac{18\!\cdots\!43}{59\!\cdots\!01}a+\frac{13\!\cdots\!14}{59\!\cdots\!01}$, $\frac{1}{29\!\cdots\!49}a^{12}-\frac{6}{29\!\cdots\!49}a^{11}-\frac{3444548211}{29\!\cdots\!49}a^{10}+\frac{17222741110}{29\!\cdots\!49}a^{9}+\frac{98\!\cdots\!57}{29\!\cdots\!49}a^{8}-\frac{39\!\cdots\!54}{29\!\cdots\!49}a^{7}-\frac{17\!\cdots\!32}{29\!\cdots\!49}a^{6}+\frac{53\!\cdots\!63}{29\!\cdots\!49}a^{5}+\frac{10\!\cdots\!99}{29\!\cdots\!49}a^{4}-\frac{20\!\cdots\!69}{29\!\cdots\!49}a^{3}-\frac{31\!\cdots\!55}{29\!\cdots\!49}a^{2}+\frac{31\!\cdots\!97}{29\!\cdots\!49}a+\frac{90\!\cdots\!98}{29\!\cdots\!49}$, $\frac{1}{29\!\cdots\!49}a^{13}-\frac{3444548247}{29\!\cdots\!49}a^{11}-\frac{3444548156}{29\!\cdots\!49}a^{10}+\frac{98\!\cdots\!17}{29\!\cdots\!49}a^{9}-\frac{47\!\cdots\!13}{29\!\cdots\!49}a^{8}-\frac{17\!\cdots\!52}{29\!\cdots\!49}a^{7}+\frac{15\!\cdots\!66}{29\!\cdots\!49}a^{6}+\frac{10\!\cdots\!78}{29\!\cdots\!49}a^{5}-\frac{11\!\cdots\!94}{29\!\cdots\!49}a^{4}-\frac{31\!\cdots\!28}{29\!\cdots\!49}a^{3}+\frac{47\!\cdots\!80}{29\!\cdots\!49}a^{2}+\frac{74\!\cdots\!46}{29\!\cdots\!49}a-\frac{61\!\cdots\!56}{29\!\cdots\!49}$, $\frac{1}{14\!\cdots\!01}a^{14}-\frac{7}{14\!\cdots\!01}a^{13}-\frac{15789084642}{14\!\cdots\!01}a^{12}+\frac{94734507943}{14\!\cdots\!01}a^{11}+\frac{10\!\cdots\!54}{14\!\cdots\!01}a^{10}-\frac{51\!\cdots\!81}{14\!\cdots\!01}a^{9}-\frac{29\!\cdots\!87}{14\!\cdots\!01}a^{8}+\frac{11\!\cdots\!93}{14\!\cdots\!01}a^{7}+\frac{12\!\cdots\!20}{14\!\cdots\!01}a^{6}-\frac{37\!\cdots\!99}{14\!\cdots\!01}a^{5}-\frac{43\!\cdots\!49}{14\!\cdots\!01}a^{4}+\frac{87\!\cdots\!05}{14\!\cdots\!01}a^{3}+\frac{16\!\cdots\!89}{14\!\cdots\!01}a^{2}-\frac{16\!\cdots\!40}{14\!\cdots\!01}a-\frac{44\!\cdots\!38}{14\!\cdots\!01}$, $\frac{1}{14\!\cdots\!01}a^{15}-\frac{15789084691}{14\!\cdots\!01}a^{13}-\frac{15789084551}{14\!\cdots\!01}a^{12}+\frac{10\!\cdots\!55}{14\!\cdots\!01}a^{11}-\frac{38\!\cdots\!04}{14\!\cdots\!01}a^{10}-\frac{29\!\cdots\!49}{14\!\cdots\!01}a^{9}+\frac{88\!\cdots\!12}{14\!\cdots\!01}a^{8}+\frac{12\!\cdots\!29}{14\!\cdots\!01}a^{7}-\frac{10\!\cdots\!94}{14\!\cdots\!01}a^{6}-\frac{43\!\cdots\!19}{14\!\cdots\!01}a^{5}+\frac{47\!\cdots\!37}{14\!\cdots\!01}a^{4}+\frac{16\!\cdots\!60}{14\!\cdots\!01}a^{3}-\frac{24\!\cdots\!80}{14\!\cdots\!01}a^{2}-\frac{36\!\cdots\!44}{14\!\cdots\!01}a+\frac{30\!\cdots\!46}{14\!\cdots\!01}$, $\frac{1}{71\!\cdots\!49}a^{16}-\frac{8}{71\!\cdots\!49}a^{15}+\frac{21244524677}{71\!\cdots\!49}a^{14}-\frac{148711672599}{71\!\cdots\!49}a^{13}+\frac{44\!\cdots\!07}{71\!\cdots\!49}a^{12}-\frac{26\!\cdots\!19}{71\!\cdots\!49}a^{11}+\frac{80\!\cdots\!42}{71\!\cdots\!49}a^{10}-\frac{40\!\cdots\!92}{71\!\cdots\!49}a^{9}+\frac{13\!\cdots\!83}{71\!\cdots\!49}a^{8}-\frac{54\!\cdots\!03}{71\!\cdots\!49}a^{7}+\frac{22\!\cdots\!90}{71\!\cdots\!49}a^{6}-\frac{66\!\cdots\!34}{71\!\cdots\!49}a^{5}+\frac{35\!\cdots\!96}{71\!\cdots\!49}a^{4}-\frac{70\!\cdots\!69}{71\!\cdots\!49}a^{3}+\frac{53\!\cdots\!73}{71\!\cdots\!49}a^{2}-\frac{53\!\cdots\!45}{71\!\cdots\!49}a+\frac{14\!\cdots\!57}{71\!\cdots\!49}$, $\frac{1}{71\!\cdots\!49}a^{17}+\frac{21244524613}{71\!\cdots\!49}a^{15}+\frac{21244524817}{71\!\cdots\!49}a^{14}+\frac{44\!\cdots\!15}{71\!\cdots\!49}a^{13}+\frac{88\!\cdots\!37}{71\!\cdots\!49}a^{12}+\frac{80\!\cdots\!90}{71\!\cdots\!49}a^{11}+\frac{24\!\cdots\!44}{71\!\cdots\!49}a^{10}+\frac{13\!\cdots\!47}{71\!\cdots\!49}a^{9}+\frac{54\!\cdots\!61}{71\!\cdots\!49}a^{8}+\frac{22\!\cdots\!66}{71\!\cdots\!49}a^{7}+\frac{11\!\cdots\!86}{71\!\cdots\!49}a^{6}+\frac{35\!\cdots\!24}{71\!\cdots\!49}a^{5}+\frac{21\!\cdots\!99}{71\!\cdots\!49}a^{4}+\frac{53\!\cdots\!21}{71\!\cdots\!49}a^{3}+\frac{37\!\cdots\!39}{71\!\cdots\!49}a^{2}-\frac{41\!\cdots\!03}{71\!\cdots\!49}a+\frac{11\!\cdots\!56}{71\!\cdots\!49}$, $\frac{1}{35\!\cdots\!01}a^{18}-\frac{9}{35\!\cdots\!01}a^{17}+\frac{8899988248}{35\!\cdots\!01}a^{16}-\frac{71199905780}{35\!\cdots\!01}a^{15}+\frac{17\!\cdots\!57}{35\!\cdots\!01}a^{14}-\frac{12\!\cdots\!63}{35\!\cdots\!01}a^{13}+\frac{25\!\cdots\!02}{35\!\cdots\!01}a^{12}-\frac{15\!\cdots\!31}{35\!\cdots\!01}a^{11}+\frac{37\!\cdots\!21}{35\!\cdots\!01}a^{10}-\frac{18\!\cdots\!82}{35\!\cdots\!01}a^{9}+\frac{53\!\cdots\!22}{35\!\cdots\!01}a^{8}-\frac{21\!\cdots\!13}{35\!\cdots\!01}a^{7}+\frac{75\!\cdots\!00}{35\!\cdots\!01}a^{6}-\frac{22\!\cdots\!07}{35\!\cdots\!01}a^{5}+\frac{10\!\cdots\!90}{35\!\cdots\!01}a^{4}-\frac{20\!\cdots\!65}{35\!\cdots\!01}a^{3}+\frac{14\!\cdots\!53}{35\!\cdots\!01}a^{2}-\frac{14\!\cdots\!44}{35\!\cdots\!01}a+\frac{22\!\cdots\!54}{35\!\cdots\!01}$, $\frac{1}{35\!\cdots\!01}a^{19}+\frac{8899988167}{35\!\cdots\!01}a^{17}+\frac{8899988452}{35\!\cdots\!01}a^{16}+\frac{17\!\cdots\!37}{35\!\cdots\!01}a^{15}+\frac{35\!\cdots\!50}{35\!\cdots\!01}a^{14}+\frac{25\!\cdots\!35}{35\!\cdots\!01}a^{13}+\frac{77\!\cdots\!87}{35\!\cdots\!01}a^{12}+\frac{37\!\cdots\!42}{35\!\cdots\!01}a^{11}+\frac{15\!\cdots\!07}{35\!\cdots\!01}a^{10}+\frac{53\!\cdots\!84}{35\!\cdots\!01}a^{9}+\frac{26\!\cdots\!85}{35\!\cdots\!01}a^{8}+\frac{75\!\cdots\!83}{35\!\cdots\!01}a^{7}+\frac{45\!\cdots\!93}{35\!\cdots\!01}a^{6}+\frac{10\!\cdots\!27}{35\!\cdots\!01}a^{5}+\frac{72\!\cdots\!45}{35\!\cdots\!01}a^{4}+\frac{14\!\cdots\!68}{35\!\cdots\!01}a^{3}+\frac{11\!\cdots\!33}{35\!\cdots\!01}a^{2}-\frac{12\!\cdots\!42}{35\!\cdots\!01}a+\frac{19\!\cdots\!86}{35\!\cdots\!01}$, $\frac{1}{17\!\cdots\!49}a^{20}-\frac{10}{17\!\cdots\!49}a^{19}-\frac{3444548180}{17\!\cdots\!49}a^{18}+\frac{31000933905}{17\!\cdots\!49}a^{17}+\frac{68\!\cdots\!61}{17\!\cdots\!49}a^{16}-\frac{54\!\cdots\!60}{17\!\cdots\!49}a^{15}+\frac{38\!\cdots\!56}{17\!\cdots\!49}a^{14}-\frac{26\!\cdots\!02}{17\!\cdots\!49}a^{13}+\frac{59\!\cdots\!78}{17\!\cdots\!49}a^{12}-\frac{35\!\cdots\!56}{17\!\cdots\!49}a^{11}+\frac{71\!\cdots\!27}{17\!\cdots\!49}a^{10}-\frac{35\!\cdots\!01}{17\!\cdots\!49}a^{9}+\frac{88\!\cdots\!99}{17\!\cdots\!49}a^{8}-\frac{35\!\cdots\!26}{17\!\cdots\!49}a^{7}+\frac{10\!\cdots\!97}{17\!\cdots\!49}a^{6}-\frac{32\!\cdots\!96}{17\!\cdots\!49}a^{5}+\frac{13\!\cdots\!88}{17\!\cdots\!49}a^{4}-\frac{27\!\cdots\!92}{17\!\cdots\!49}a^{3}+\frac{16\!\cdots\!85}{17\!\cdots\!49}a^{2}-\frac{16\!\cdots\!74}{17\!\cdots\!49}a+\frac{20\!\cdots\!64}{17\!\cdots\!49}$, $\frac{1}{17\!\cdots\!49}a^{21}-\frac{3444548280}{17\!\cdots\!49}a^{19}-\frac{3444547895}{17\!\cdots\!49}a^{18}+\frac{68\!\cdots\!11}{17\!\cdots\!49}a^{17}+\frac{13\!\cdots\!50}{17\!\cdots\!49}a^{16}+\frac{38\!\cdots\!56}{17\!\cdots\!49}a^{15}+\frac{11\!\cdots\!58}{17\!\cdots\!49}a^{14}+\frac{20\!\cdots\!02}{60\!\cdots\!81}a^{13}+\frac{23\!\cdots\!24}{17\!\cdots\!49}a^{12}+\frac{71\!\cdots\!67}{17\!\cdots\!49}a^{11}+\frac{35\!\cdots\!69}{17\!\cdots\!49}a^{10}+\frac{88\!\cdots\!89}{17\!\cdots\!49}a^{9}+\frac{53\!\cdots\!64}{17\!\cdots\!49}a^{8}+\frac{10\!\cdots\!37}{17\!\cdots\!49}a^{7}+\frac{76\!\cdots\!74}{17\!\cdots\!49}a^{6}+\frac{13\!\cdots\!28}{17\!\cdots\!49}a^{5}+\frac{37\!\cdots\!72}{60\!\cdots\!81}a^{4}+\frac{16\!\cdots\!65}{17\!\cdots\!49}a^{3}+\frac{15\!\cdots\!76}{17\!\cdots\!49}a^{2}-\frac{14\!\cdots\!76}{17\!\cdots\!49}a+\frac{20\!\cdots\!40}{17\!\cdots\!49}$
Monogenic: | Not computed | |
Index: | $1$ | |
Inessential primes: | None |
Class group and class number
not computed
Unit group
Rank: | $19$ | sage: UK.rank()
gp: K.fu
magma: UnitRank(K);
oscar: rank(UK)
| |
Torsion generator: | \( -1 \) (order $2$) | 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 $
Galois group
$C_2^{10}.S_{11}$ (as 22T51):
A non-solvable group of order 40874803200 |
The 376 conjugacy class representatives for $C_2^{10}.S_{11}$ are not computed |
Character table for $C_2^{10}.S_{11}$ is not computed |
Intermediate fields
11.9.8692675390643.1 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Sibling fields
Frobenius cycle types
$p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Cycle type | ${\href{/padicField/2.6.0.1}{6} }^{2}{,}\,{\href{/padicField/2.5.0.1}{5} }^{2}$ | ${\href{/padicField/3.11.0.1}{11} }^{2}$ | ${\href{/padicField/5.12.0.1}{12} }{,}\,{\href{/padicField/5.10.0.1}{10} }$ | ${\href{/padicField/7.12.0.1}{12} }{,}\,{\href{/padicField/7.8.0.1}{8} }{,}\,{\href{/padicField/7.1.0.1}{1} }^{2}$ | ${\href{/padicField/11.11.0.1}{11} }^{2}$ | ${\href{/padicField/13.11.0.1}{11} }^{2}$ | $18{,}\,{\href{/padicField/17.4.0.1}{4} }$ | ${\href{/padicField/19.8.0.1}{8} }^{2}{,}\,{\href{/padicField/19.3.0.1}{3} }^{2}$ | ${\href{/padicField/23.6.0.1}{6} }^{2}{,}\,{\href{/padicField/23.3.0.1}{3} }^{2}{,}\,{\href{/padicField/23.2.0.1}{2} }^{2}$ | R | ${\href{/padicField/31.12.0.1}{12} }{,}\,{\href{/padicField/31.10.0.1}{10} }$ | ${\href{/padicField/37.6.0.1}{6} }^{2}{,}\,{\href{/padicField/37.4.0.1}{4} }^{2}{,}\,{\href{/padicField/37.1.0.1}{1} }^{2}$ | ${\href{/padicField/41.11.0.1}{11} }^{2}$ | ${\href{/padicField/43.11.0.1}{11} }^{2}$ | ${\href{/padicField/47.8.0.1}{8} }{,}\,{\href{/padicField/47.4.0.1}{4} }{,}\,{\href{/padicField/47.2.0.1}{2} }^{4}{,}\,{\href{/padicField/47.1.0.1}{1} }^{2}$ | ${\href{/padicField/53.12.0.1}{12} }{,}\,{\href{/padicField/53.8.0.1}{8} }{,}\,{\href{/padicField/53.1.0.1}{1} }^{2}$ | $20{,}\,{\href{/padicField/59.2.0.1}{2} }$ |
In the table, R denotes a ramified prime. Cycle lengths which are repeated in a cycle type are indicated by exponents.
Local algebras for ramified primes
$p$ | Label | Polynomial | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
\(29\) | 29.2.0.1 | $x^{2} + 24 x + 2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ |
29.4.2.2 | $x^{4} - 696 x^{2} + 1682$ | $2$ | $2$ | $2$ | $C_4$ | $[\ ]_{2}^{2}$ | |
29.16.8.1 | $x^{16} + 5568 x^{15} + 13563880 x^{14} + 18881728320 x^{13} + 16428480372226 x^{12} + 9148801553592528 x^{11} + 3184735792552646192 x^{10} + 633724384469595120286 x^{9} + 55249468166464640094225 x^{8} + 18378034980956595686936 x^{7} + 2688132351641987586456 x^{6} + 2199337349954841447326 x^{5} + 180719728922044973705920 x^{4} + 1366890777105246403746256 x^{3} + 1613855339675279772970993 x^{2} + 1393970274901245210856928 x + 165405867866431160098509$ | $2$ | $8$ | $8$ | $C_8\times C_2$ | $[\ ]_{2}^{8}$ | |
\(151\) | $\Q_{151}$ | $x + 145$ | $1$ | $1$ | $0$ | Trivial | $[\ ]$ |
$\Q_{151}$ | $x + 145$ | $1$ | $1$ | $0$ | Trivial | $[\ ]$ | |
151.2.1.1 | $x^{2} + 453$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | |
151.2.1.1 | $x^{2} + 453$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | |
151.8.0.1 | $x^{8} + 9 x^{4} + 140 x^{3} + 122 x^{2} + 43 x + 6$ | $1$ | $8$ | $0$ | $C_8$ | $[\ ]^{8}$ | |
151.8.0.1 | $x^{8} + 9 x^{4} + 140 x^{3} + 122 x^{2} + 43 x + 6$ | $1$ | $8$ | $0$ | $C_8$ | $[\ ]^{8}$ | |
\(2311\) | Deg $2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ | |
Deg $2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ | ||
Deg $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | ||
Deg $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | ||
Deg $7$ | $1$ | $7$ | $0$ | $C_7$ | $[\ ]^{7}$ | ||
Deg $7$ | $1$ | $7$ | $0$ | $C_7$ | $[\ ]^{7}$ | ||
\(24910163\) | Deg $2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ | |
Deg $2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ | ||
Deg $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | ||
Deg $2$ | $2$ | $1$ | $1$ | $C_2$ | $[\ ]_{2}$ | ||
Deg $7$ | $1$ | $7$ | $0$ | $C_7$ | $[\ ]^{7}$ | ||
Deg $7$ | $1$ | $7$ | $0$ | $C_7$ | $[\ ]^{7}$ | ||
\(1702694681\) | Deg $2$ | $1$ | $2$ | $0$ | $C_2$ | $[\ ]^{2}$ | |
Deg $4$ | $2$ | $2$ | $2$ | ||||
Deg $16$ | $2$ | $8$ | $8$ |