Normalized defining polynomial
\( x^{18} - 3 x^{17} - 15 x^{16} + 69 x^{15} - 846 x^{14} + 3867 x^{13} + 16107 x^{12} + 46644 x^{11} + \cdots - 1600 \)
Invariants
| Degree: | $18$ |
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| Signature: | $[6, 6]$ |
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| Discriminant: |
\(21655026155451642797719955871000000000000\)
\(\medspace = 2^{12}\cdot 3^{24}\cdot 5^{12}\cdot 11^{6}\cdot 3511^{3}\)
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| Root discriminant: | \(174.13\) |
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| Galois root discriminant: | not computed | ||
| Ramified primes: |
\(2\), \(3\), \(5\), \(11\), \(3511\)
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| Discriminant root field: | \(\Q(\sqrt{3511}) \) | ||
| $\Aut(K/\Q)$: | $C_1$ |
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| This field is not Galois over $\Q$. | |||
| This is not a CM field. | |||
| This field has no CM subfields. | |||
Integral basis (with respect to field generator \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $\frac{1}{2}a^{10}-\frac{1}{2}a^{9}-\frac{1}{2}a^{8}-\frac{1}{2}a^{7}-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-\frac{1}{2}a^{2}$, $\frac{1}{2}a^{11}-\frac{1}{2}a^{7}-\frac{1}{2}a^{6}-\frac{1}{2}a^{4}-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}$, $\frac{1}{4}a^{12}-\frac{1}{4}a^{11}-\frac{1}{4}a^{10}-\frac{1}{4}a^{9}-\frac{1}{4}a^{7}+\frac{1}{4}a^{6}-\frac{1}{2}a^{5}+\frac{1}{4}a^{4}-\frac{1}{2}a^{2}$, $\frac{1}{4}a^{13}+\frac{1}{4}a^{9}+\frac{1}{4}a^{8}+\frac{1}{4}a^{6}+\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{1}{2}a^{2}$, $\frac{1}{40}a^{14}-\frac{3}{40}a^{13}-\frac{1}{8}a^{12}-\frac{1}{40}a^{11}+\frac{1}{10}a^{10}-\frac{3}{40}a^{9}+\frac{7}{40}a^{8}-\frac{3}{20}a^{7}+\frac{3}{8}a^{6}+\frac{1}{4}a^{5}-\frac{1}{10}a^{4}-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}$, $\frac{1}{40}a^{15}-\frac{1}{10}a^{13}+\frac{1}{10}a^{12}+\frac{1}{40}a^{11}+\frac{9}{40}a^{10}+\frac{1}{5}a^{9}+\frac{1}{8}a^{8}+\frac{17}{40}a^{7}-\frac{3}{8}a^{6}+\frac{2}{5}a^{5}-\frac{1}{20}a^{4}-\frac{1}{2}a^{3}$, $\frac{1}{80}a^{16}-\frac{1}{80}a^{15}-\frac{1}{80}a^{14}-\frac{1}{80}a^{13}-\frac{1}{10}a^{12}-\frac{1}{16}a^{11}+\frac{1}{80}a^{10}+\frac{9}{40}a^{9}-\frac{7}{80}a^{8}+\frac{1}{4}a^{7}-\frac{17}{40}a^{6}-\frac{1}{10}a^{5}-\frac{1}{4}a^{4}-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}$, $\frac{1}{79\cdots 80}a^{17}+\frac{46\cdots 11}{79\cdots 80}a^{16}+\frac{71\cdots 19}{79\cdots 80}a^{15}-\frac{83\cdots 81}{79\cdots 80}a^{14}-\frac{19\cdots 41}{19\cdots 20}a^{13}+\frac{95\cdots 67}{79\cdots 80}a^{12}-\frac{15\cdots 39}{79\cdots 80}a^{11}-\frac{89\cdots 27}{39\cdots 40}a^{10}-\frac{31\cdots 91}{79\cdots 80}a^{9}-\frac{42\cdots 53}{19\cdots 92}a^{8}+\frac{79\cdots 09}{39\cdots 40}a^{7}+\frac{51\cdots 11}{19\cdots 20}a^{6}-\frac{11\cdots 49}{49\cdots 80}a^{5}-\frac{96\cdots 99}{99\cdots 60}a^{4}+\frac{15\cdots 35}{99\cdots 96}a^{3}-\frac{19\cdots 43}{99\cdots 96}a^{2}+\frac{44\cdots 23}{99\cdots 96}a-\frac{13\cdots 67}{49\cdots 98}$
| Monogenic: | No | |
| Index: | Not computed | |
| Inessential primes: | $2$ |
Class group and class number
| Ideal class group: | Trivial group, which has order $1$ (assuming GRH) |
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| Narrow class group: | $C_{2}$, which has order $2$ (assuming GRH) |
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Unit group
| Rank: | $11$ |
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| Torsion generator: |
\( -1 \)
(order $2$)
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| Fundamental units: |
$\frac{16\cdots 67}{24\cdots 80}a^{17}-\frac{47\cdots 59}{24\cdots 80}a^{16}-\frac{24\cdots 51}{24\cdots 80}a^{15}+\frac{11\cdots 13}{24\cdots 80}a^{14}-\frac{34\cdots 91}{60\cdots 20}a^{13}+\frac{62\cdots 97}{24\cdots 80}a^{12}+\frac{26\cdots 23}{24\cdots 80}a^{11}+\frac{39\cdots 71}{12\cdots 40}a^{10}+\frac{63\cdots 63}{24\cdots 80}a^{9}-\frac{23\cdots 37}{60\cdots 92}a^{8}+\frac{43\cdots 91}{12\cdots 40}a^{7}+\frac{24\cdots 33}{60\cdots 20}a^{6}-\frac{81\cdots 97}{15\cdots 98}a^{5}-\frac{34\cdots 71}{60\cdots 92}a^{4}+\frac{56\cdots 63}{30\cdots 96}a^{3}+\frac{52\cdots 25}{30\cdots 96}a^{2}+\frac{16\cdots 85}{30\cdots 96}a+\frac{20\cdots 79}{15\cdots 98}$, $\frac{16\cdots 89}{79\cdots 80}a^{17}-\frac{10\cdots 85}{15\cdots 36}a^{16}-\frac{22\cdots 89}{79\cdots 80}a^{15}+\frac{24\cdots 55}{15\cdots 36}a^{14}-\frac{17\cdots 37}{99\cdots 60}a^{13}+\frac{67\cdots 99}{79\cdots 80}a^{12}+\frac{48\cdots 65}{15\cdots 36}a^{11}+\frac{34\cdots 07}{39\cdots 40}a^{10}+\frac{60\cdots 17}{79\cdots 80}a^{9}-\frac{29\cdots 33}{19\cdots 20}a^{8}+\frac{63\cdots 97}{39\cdots 40}a^{7}+\frac{16\cdots 03}{19\cdots 20}a^{6}-\frac{53\cdots 39}{24\cdots 90}a^{5}-\frac{17\cdots 95}{19\cdots 92}a^{4}+\frac{11\cdots 45}{99\cdots 96}a^{3}+\frac{52\cdots 79}{99\cdots 96}a^{2}-\frac{23\cdots 53}{99\cdots 96}a+\frac{89\cdots 91}{49\cdots 98}$, $\frac{13\cdots 91}{49\cdots 80}a^{17}-\frac{17\cdots 21}{19\cdots 20}a^{16}-\frac{15\cdots 87}{39\cdots 84}a^{15}+\frac{39\cdots 47}{19\cdots 20}a^{14}-\frac{93\cdots 93}{39\cdots 84}a^{13}+\frac{10\cdots 37}{99\cdots 60}a^{12}+\frac{82\cdots 87}{19\cdots 20}a^{11}+\frac{23\cdots 39}{19\cdots 20}a^{10}+\frac{50\cdots 33}{49\cdots 98}a^{9}-\frac{37\cdots 03}{19\cdots 20}a^{8}+\frac{97\cdots 11}{49\cdots 80}a^{7}+\frac{60\cdots 09}{49\cdots 80}a^{6}-\frac{33\cdots 12}{12\cdots 95}a^{5}-\frac{14\cdots 83}{99\cdots 96}a^{4}+\frac{33\cdots 27}{24\cdots 99}a^{3}+\frac{56\cdots 26}{24\cdots 99}a^{2}+\frac{75\cdots 58}{24\cdots 99}a-\frac{44\cdots 13}{24\cdots 99}$, $\frac{40\cdots 73}{79\cdots 80}a^{17}-\frac{97\cdots 29}{79\cdots 80}a^{16}-\frac{69\cdots 17}{79\cdots 80}a^{15}+\frac{24\cdots 83}{79\cdots 80}a^{14}-\frac{82\cdots 67}{19\cdots 20}a^{13}+\frac{13\cdots 43}{79\cdots 80}a^{12}+\frac{75\cdots 73}{79\cdots 80}a^{11}+\frac{11\cdots 29}{39\cdots 40}a^{10}+\frac{16\cdots 41}{79\cdots 80}a^{9}-\frac{19\cdots 41}{99\cdots 60}a^{8}+\frac{40\cdots 69}{39\cdots 40}a^{7}+\frac{19\cdots 47}{39\cdots 84}a^{6}-\frac{66\cdots 41}{24\cdots 90}a^{5}-\frac{13\cdots 29}{19\cdots 92}a^{4}-\frac{46\cdots 95}{99\cdots 96}a^{3}+\frac{20\cdots 61}{99\cdots 96}a^{2}+\frac{73\cdots 63}{99\cdots 96}a+\frac{63\cdots 71}{49\cdots 98}$, $\frac{77\cdots 95}{15\cdots 36}a^{17}-\frac{25\cdots 15}{15\cdots 36}a^{16}-\frac{10\cdots 35}{15\cdots 36}a^{15}+\frac{56\cdots 29}{15\cdots 36}a^{14}-\frac{84\cdots 77}{19\cdots 92}a^{13}+\frac{31\cdots 45}{15\cdots 36}a^{12}+\frac{11\cdots 71}{15\cdots 36}a^{11}+\frac{16\cdots 77}{79\cdots 68}a^{10}+\frac{28\cdots 51}{15\cdots 36}a^{9}-\frac{13\cdots 09}{39\cdots 84}a^{8}+\frac{29\cdots 95}{79\cdots 68}a^{7}+\frac{81\cdots 05}{39\cdots 84}a^{6}-\frac{25\cdots 31}{49\cdots 98}a^{5}-\frac{40\cdots 89}{19\cdots 92}a^{4}+\frac{27\cdots 51}{99\cdots 96}a^{3}-\frac{16\cdots 85}{99\cdots 96}a^{2}-\frac{10\cdots 15}{99\cdots 96}a+\frac{32\cdots 81}{49\cdots 98}$, $\frac{10\cdots 61}{15\cdots 36}a^{17}-\frac{18\cdots 41}{79\cdots 80}a^{16}-\frac{73\cdots 89}{79\cdots 80}a^{15}+\frac{40\cdots 87}{79\cdots 80}a^{14}-\frac{11\cdots 63}{19\cdots 20}a^{13}+\frac{22\cdots 63}{79\cdots 80}a^{12}+\frac{77\cdots 49}{79\cdots 80}a^{11}+\frac{10\cdots 29}{39\cdots 40}a^{10}+\frac{19\cdots 49}{79\cdots 80}a^{9}-\frac{53\cdots 67}{99\cdots 60}a^{8}+\frac{23\cdots 37}{39\cdots 40}a^{7}+\frac{45\cdots 01}{19\cdots 20}a^{6}-\frac{39\cdots 17}{49\cdots 80}a^{5}-\frac{20\cdots 03}{99\cdots 60}a^{4}+\frac{49\cdots 03}{99\cdots 96}a^{3}-\frac{31\cdots 43}{99\cdots 96}a^{2}-\frac{30\cdots 53}{99\cdots 96}a-\frac{21\cdots 19}{49\cdots 98}$, $\frac{41\cdots 73}{79\cdots 80}a^{17}-\frac{82\cdots 57}{79\cdots 80}a^{16}-\frac{71\cdots 01}{79\cdots 80}a^{15}+\frac{43\cdots 99}{15\cdots 36}a^{14}-\frac{83\cdots 21}{19\cdots 20}a^{13}+\frac{12\cdots 79}{79\cdots 80}a^{12}+\frac{80\cdots 57}{79\cdots 80}a^{11}+\frac{13\cdots 69}{39\cdots 40}a^{10}+\frac{18\cdots 29}{79\cdots 80}a^{9}-\frac{19\cdots 07}{24\cdots 90}a^{8}+\frac{17\cdots 41}{79\cdots 68}a^{7}+\frac{10\cdots 73}{19\cdots 20}a^{6}+\frac{44\cdots 51}{49\cdots 98}a^{5}-\frac{30\cdots 49}{99\cdots 60}a^{4}-\frac{11\cdots 39}{99\cdots 96}a^{3}-\frac{13\cdots 17}{99\cdots 96}a^{2}+\frac{32\cdots 71}{99\cdots 96}a+\frac{40\cdots 57}{49\cdots 98}$, $\frac{11\cdots 81}{79\cdots 80}a^{17}-\frac{21\cdots 61}{79\cdots 80}a^{16}-\frac{19\cdots 01}{79\cdots 80}a^{15}+\frac{57\cdots 03}{79\cdots 80}a^{14}-\frac{45\cdots 49}{39\cdots 84}a^{13}+\frac{68\cdots 79}{15\cdots 36}a^{12}+\frac{22\cdots 97}{79\cdots 80}a^{11}+\frac{39\cdots 37}{39\cdots 40}a^{10}+\frac{52\cdots 61}{79\cdots 80}a^{9}-\frac{15\cdots 69}{99\cdots 60}a^{8}+\frac{22\cdots 01}{39\cdots 40}a^{7}+\frac{30\cdots 33}{19\cdots 20}a^{6}+\frac{18\cdots 41}{49\cdots 98}a^{5}-\frac{83\cdots 17}{99\cdots 60}a^{4}-\frac{38\cdots 75}{99\cdots 96}a^{3}-\frac{50\cdots 27}{99\cdots 96}a^{2}+\frac{80\cdots 83}{99\cdots 96}a+\frac{16\cdots 61}{49\cdots 98}$, $\frac{11\cdots 67}{15\cdots 36}a^{17}+\frac{90\cdots 45}{15\cdots 36}a^{16}-\frac{77\cdots 83}{79\cdots 80}a^{15}+\frac{55\cdots 37}{15\cdots 36}a^{14}+\frac{52\cdots 33}{19\cdots 20}a^{13}-\frac{15\cdots 47}{79\cdots 80}a^{12}+\frac{28\cdots 27}{79\cdots 80}a^{11}-\frac{42\cdots 61}{39\cdots 40}a^{10}+\frac{19\cdots 11}{79\cdots 80}a^{9}+\frac{59\cdots 79}{99\cdots 96}a^{8}-\frac{74\cdots 93}{39\cdots 40}a^{7}+\frac{12\cdots 35}{39\cdots 84}a^{6}-\frac{10\cdots 43}{49\cdots 80}a^{5}+\frac{11\cdots 87}{99\cdots 60}a^{4}+\frac{21\cdots 03}{99\cdots 96}a^{3}+\frac{74\cdots 29}{99\cdots 96}a^{2}-\frac{21\cdots 51}{99\cdots 96}a-\frac{15\cdots 85}{49\cdots 98}$, $\frac{53\cdots 33}{79\cdots 80}a^{17}-\frac{12\cdots 01}{79\cdots 80}a^{16}-\frac{89\cdots 81}{79\cdots 80}a^{15}+\frac{30\cdots 07}{79\cdots 80}a^{14}-\frac{54\cdots 51}{99\cdots 60}a^{13}+\frac{35\cdots 47}{15\cdots 36}a^{12}+\frac{19\cdots 61}{15\cdots 36}a^{11}+\frac{32\cdots 47}{79\cdots 68}a^{10}+\frac{22\cdots 01}{79\cdots 80}a^{9}-\frac{81\cdots 47}{39\cdots 84}a^{8}+\frac{94\cdots 77}{39\cdots 40}a^{7}+\frac{11\cdots 97}{19\cdots 20}a^{6}-\frac{44\cdots 81}{24\cdots 90}a^{5}-\frac{63\cdots 37}{99\cdots 60}a^{4}-\frac{20\cdots 17}{99\cdots 96}a^{3}-\frac{21\cdots 69}{99\cdots 96}a^{2}+\frac{64\cdots 51}{99\cdots 96}a+\frac{73\cdots 01}{49\cdots 98}$, $\frac{16\cdots 07}{79\cdots 80}a^{17}-\frac{12\cdots 39}{79\cdots 80}a^{16}+\frac{32\cdots 37}{79\cdots 80}a^{15}-\frac{27\cdots 19}{79\cdots 80}a^{14}-\frac{39\cdots 01}{24\cdots 99}a^{13}+\frac{12\cdots 09}{79\cdots 80}a^{12}-\frac{30\cdots 37}{79\cdots 80}a^{11}+\frac{10\cdots 73}{39\cdots 40}a^{10}-\frac{30\cdots 17}{79\cdots 80}a^{9}+\frac{55\cdots 49}{19\cdots 20}a^{8}+\frac{21\cdots 95}{79\cdots 68}a^{7}-\frac{78\cdots 57}{19\cdots 20}a^{6}-\frac{34\cdots 53}{12\cdots 95}a^{5}+\frac{22\cdots 99}{99\cdots 60}a^{4}+\frac{29\cdots 15}{99\cdots 96}a^{3}+\frac{51\cdots 31}{99\cdots 96}a^{2}-\frac{37\cdots 87}{99\cdots 96}a+\frac{81\cdots 01}{49\cdots 98}$
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| Regulator: | \( 49924278928300 \) (assuming GRH) |
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Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{6}\cdot(2\pi)^{6}\cdot 49924278928300 \cdot 1}{2\cdot\sqrt{21655026155451642797719955871000000000000}}\cr\approx \mathstrut & 0.667977190927831 \end{aligned}\] (assuming GRH)
Galois group
$C_3^4:(C_6^2:C_4)$ (as 18T576):
| A solvable group of order 11664 |
| The 49 conjugacy class representatives for $C_3^4:(C_6^2:C_4)$ |
| Character table for $C_3^4:(C_6^2:C_4)$ |
Intermediate fields
| \(\Q(\sqrt{5}) \), 6.6.55130625.1 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Sibling fields
| Degree 18 sibling: | data not computed |
| Degree 36 siblings: | 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 | R | R | ${\href{/padicField/7.4.0.1}{4} }^{3}{,}\,{\href{/padicField/7.2.0.1}{2} }^{3}$ | R | ${\href{/padicField/13.12.0.1}{12} }{,}\,{\href{/padicField/13.6.0.1}{6} }$ | ${\href{/padicField/17.4.0.1}{4} }^{3}{,}\,{\href{/padicField/17.2.0.1}{2} }^{3}$ | ${\href{/padicField/19.6.0.1}{6} }^{2}{,}\,{\href{/padicField/19.3.0.1}{3} }{,}\,{\href{/padicField/19.2.0.1}{2} }{,}\,{\href{/padicField/19.1.0.1}{1} }$ | ${\href{/padicField/23.12.0.1}{12} }{,}\,{\href{/padicField/23.4.0.1}{4} }{,}\,{\href{/padicField/23.2.0.1}{2} }$ | ${\href{/padicField/29.6.0.1}{6} }{,}\,{\href{/padicField/29.3.0.1}{3} }^{4}$ | ${\href{/padicField/31.3.0.1}{3} }^{6}$ | ${\href{/padicField/37.12.0.1}{12} }{,}\,{\href{/padicField/37.6.0.1}{6} }$ | ${\href{/padicField/41.2.0.1}{2} }^{7}{,}\,{\href{/padicField/41.1.0.1}{1} }^{4}$ | ${\href{/padicField/43.12.0.1}{12} }{,}\,{\href{/padicField/43.4.0.1}{4} }{,}\,{\href{/padicField/43.2.0.1}{2} }$ | ${\href{/padicField/47.4.0.1}{4} }^{4}{,}\,{\href{/padicField/47.2.0.1}{2} }$ | ${\href{/padicField/53.12.0.1}{12} }{,}\,{\href{/padicField/53.6.0.1}{6} }$ | ${\href{/padicField/59.6.0.1}{6} }{,}\,{\href{/padicField/59.3.0.1}{3} }^{4}$ |
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 |
|---|---|---|---|---|---|---|---|
|
\(2\)
| 2.2.1.0a1.1 | $x^{2} + x + 1$ | $1$ | $2$ | $0$ | $C_2$ | $$[\ ]^{2}$$ |
| 2.2.2.4a2.2 | $x^{4} + 4 x^{3} + 5 x^{2} + 4 x + 7$ | $2$ | $2$ | $4$ | $D_{4}$ | $$[2, 2]^{2}$$ | |
| 2.4.1.0a1.1 | $x^{4} + x + 1$ | $1$ | $4$ | $0$ | $C_4$ | $$[\ ]^{4}$$ | |
| 2.4.2.8a3.1 | $x^{8} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 2 x^{3} + 5 x^{2} + 4 x + 3$ | $2$ | $4$ | $8$ | $C_2^2:C_4$ | $$[2, 2]^{4}$$ | |
|
\(3\)
| 3.2.9.24a21.1 | $x^{18} + 18 x^{17} + 162 x^{16} + 960 x^{15} + 4176 x^{14} + 14112 x^{13} + 38304 x^{12} + 85248 x^{11} + 157536 x^{10} + 243398 x^{9} + 315123 x^{8} + 341214 x^{7} + 307044 x^{6} + 226956 x^{5} + 135192 x^{4} + 62904 x^{3} + 21648 x^{2} + 4944 x + 563$ | $9$ | $2$ | $24$ | 18T95 | not computed |
|
\(5\)
| 5.1.2.1a1.1 | $x^{2} + 5$ | $2$ | $1$ | $1$ | $C_2$ | $$[\ ]_{2}$$ |
| 5.2.2.2a1.2 | $x^{4} + 8 x^{3} + 20 x^{2} + 16 x + 9$ | $2$ | $2$ | $2$ | $C_2^2$ | $$[\ ]_{2}^{2}$$ | |
| 5.1.4.3a1.4 | $x^{4} + 20$ | $4$ | $1$ | $3$ | $C_4$ | $$[\ ]_{4}$$ | |
| 5.2.4.6a1.2 | $x^{8} + 16 x^{7} + 104 x^{6} + 352 x^{5} + 664 x^{4} + 704 x^{3} + 416 x^{2} + 128 x + 21$ | $4$ | $2$ | $6$ | $C_4\times C_2$ | $$[\ ]_{4}^{2}$$ | |
|
\(11\)
| 11.1.3.2a1.1 | $x^{3} + 11$ | $3$ | $1$ | $2$ | $S_3$ | $$[\ ]_{3}^{2}$$ |
| 11.3.1.0a1.1 | $x^{3} + 2 x + 9$ | $1$ | $3$ | $0$ | $C_3$ | $$[\ ]^{3}$$ | |
| 11.2.3.4a1.2 | $x^{6} + 21 x^{5} + 153 x^{4} + 427 x^{3} + 306 x^{2} + 84 x + 19$ | $3$ | $2$ | $4$ | $S_3$ | $$[\ ]_{3}^{2}$$ | |
| 11.6.1.0a1.1 | $x^{6} + 3 x^{4} + 4 x^{3} + 6 x^{2} + 7 x + 2$ | $1$ | $6$ | $0$ | $C_6$ | $$[\ ]^{6}$$ | |
|
\(3511\)
| Deg $3$ | $1$ | $3$ | $0$ | $C_3$ | $$[\ ]^{3}$$ | |
| Deg $3$ | $1$ | $3$ | $0$ | $C_3$ | $$[\ ]^{3}$$ | ||
| Deg $6$ | $1$ | $6$ | $0$ | $C_6$ | $$[\ ]^{6}$$ | ||
| Deg $6$ | $2$ | $3$ | $3$ |