Normalized defining polynomial
\( x^{20} - 6 x^{19} + 216 x^{18} - 1093 x^{17} + 19018 x^{16} - 81544 x^{15} + 888786 x^{14} + \cdots + 21376757978 \)
Invariants
| Degree: | $20$ |
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| Signature: | $(0, 10)$ |
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| Discriminant: |
\(5117380860656444079832785566505699574289404854272\)
\(\medspace = 2^{16}\cdot 7^{15}\cdot 11^{15}\cdot 13^{14}\)
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| Root discriminant: | \(272.55\) |
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| Galois root discriminant: | not computed | ||
| Ramified primes: |
\(2\), \(7\), \(11\), \(13\)
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| Discriminant root field: | \(\Q(\sqrt{77}) \) | ||
| $\Aut(K/\Q)$: | $C_2$ |
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| This field is not Galois over $\Q$. | |||
| This is not a CM field. | |||
| Maximal CM subfield: | \(\Q(\sqrt{-77 +2 \sqrt{1001}})\) | ||
Integral basis (with respect to field generator \(a\))
$1$, $a$, $a^{2}$, $a^{3}$, $a^{4}$, $a^{5}$, $a^{6}$, $a^{7}$, $a^{8}$, $a^{9}$, $a^{10}$, $a^{11}$, $\frac{1}{13}a^{12}+\frac{2}{13}a^{11}-\frac{3}{13}a^{10}-\frac{3}{13}a^{9}-\frac{5}{13}a^{8}-\frac{5}{13}a^{7}-\frac{5}{13}a^{6}+\frac{4}{13}a^{5}+\frac{2}{13}a^{4}-\frac{4}{13}a^{3}-\frac{2}{13}a^{2}-\frac{4}{13}a-\frac{1}{13}$, $\frac{1}{13}a^{13}+\frac{6}{13}a^{11}+\frac{3}{13}a^{10}+\frac{1}{13}a^{9}+\frac{5}{13}a^{8}+\frac{5}{13}a^{7}+\frac{1}{13}a^{6}-\frac{6}{13}a^{5}+\frac{5}{13}a^{4}+\frac{6}{13}a^{3}-\frac{6}{13}a+\frac{2}{13}$, $\frac{1}{221}a^{14}+\frac{7}{221}a^{13}+\frac{4}{221}a^{12}-\frac{11}{221}a^{11}+\frac{2}{221}a^{10}+\frac{83}{221}a^{9}+\frac{89}{221}a^{8}-\frac{58}{221}a^{7}+\frac{50}{221}a^{6}-\frac{32}{221}a^{5}-\frac{15}{221}a^{4}-\frac{28}{221}a^{3}+\frac{24}{221}a^{2}-\frac{19}{221}a-\frac{10}{221}$, $\frac{1}{1105}a^{15}-\frac{2}{1105}a^{14}-\frac{42}{1105}a^{13}+\frac{4}{1105}a^{12}+\frac{526}{1105}a^{11}-\frac{37}{1105}a^{10}+\frac{18}{221}a^{9}-\frac{29}{221}a^{8}+\frac{402}{1105}a^{7}-\frac{499}{1105}a^{6}-\frac{288}{1105}a^{5}-\frac{369}{1105}a^{4}+\frac{174}{1105}a^{3}+\frac{547}{1105}a^{2}+\frac{297}{1105}a-\frac{369}{1105}$, $\frac{1}{1105}a^{16}-\frac{1}{1105}a^{14}-\frac{4}{221}a^{13}+\frac{2}{65}a^{12}-\frac{32}{221}a^{11}+\frac{276}{1105}a^{10}+\frac{6}{221}a^{9}-\frac{388}{1105}a^{8}-\frac{36}{221}a^{7}-\frac{311}{1105}a^{6}-\frac{4}{17}a^{5}+\frac{42}{85}a^{4}-\frac{56}{221}a^{3}+\frac{516}{1105}a^{2}+\frac{61}{221}a+\frac{87}{1105}$, $\frac{1}{1105}a^{17}-\frac{2}{1105}a^{14}-\frac{38}{1105}a^{13}+\frac{9}{1105}a^{12}-\frac{268}{1105}a^{11}+\frac{373}{1105}a^{10}-\frac{168}{1105}a^{9}+\frac{36}{221}a^{8}-\frac{134}{1105}a^{7}-\frac{354}{1105}a^{6}-\frac{127}{1105}a^{5}-\frac{524}{1105}a^{4}-\frac{25}{221}a^{3}+\frac{57}{1105}a^{2}-\frac{421}{1105}a+\frac{111}{1105}$, $\frac{1}{51\cdots 05}a^{18}-\frac{50\cdots 03}{51\cdots 05}a^{17}+\frac{17\cdots 29}{51\cdots 05}a^{16}+\frac{14\cdots 37}{51\cdots 05}a^{15}-\frac{36\cdots 74}{51\cdots 05}a^{14}+\frac{34\cdots 99}{10\cdots 81}a^{13}+\frac{18\cdots 77}{51\cdots 05}a^{12}+\frac{25\cdots 66}{51\cdots 05}a^{11}+\frac{14\cdots 64}{51\cdots 05}a^{10}+\frac{14\cdots 34}{51\cdots 05}a^{9}+\frac{22\cdots 44}{51\cdots 05}a^{8}-\frac{92\cdots 89}{51\cdots 05}a^{7}-\frac{98\cdots 33}{10\cdots 81}a^{6}+\frac{17\cdots 92}{10\cdots 81}a^{5}+\frac{20\cdots 08}{79\cdots 37}a^{4}-\frac{20\cdots 67}{51\cdots 05}a^{3}+\frac{20\cdots 56}{10\cdots 81}a^{2}-\frac{30\cdots 18}{51\cdots 05}a+\frac{79\cdots 79}{51\cdots 05}$, $\frac{1}{22\cdots 45}a^{19}+\frac{10\cdots 18}{34\cdots 93}a^{18}-\frac{13\cdots 59}{44\cdots 09}a^{17}+\frac{16\cdots 80}{44\cdots 09}a^{16}-\frac{36\cdots 32}{22\cdots 45}a^{15}+\frac{40\cdots 77}{44\cdots 09}a^{14}+\frac{63\cdots 92}{44\cdots 09}a^{13}+\frac{64\cdots 85}{44\cdots 09}a^{12}+\frac{30\cdots 58}{57\cdots 95}a^{11}-\frac{11\cdots 75}{26\cdots 77}a^{10}-\frac{57\cdots 44}{22\cdots 45}a^{9}+\frac{17\cdots 76}{44\cdots 09}a^{8}-\frac{98\cdots 39}{44\cdots 09}a^{7}+\frac{88\cdots 53}{44\cdots 09}a^{6}+\frac{39\cdots 54}{97\cdots 15}a^{5}-\frac{23\cdots 40}{19\cdots 83}a^{4}-\frac{74\cdots 57}{22\cdots 45}a^{3}-\frac{17\cdots 68}{44\cdots 09}a^{2}-\frac{37\cdots 88}{22\cdots 45}a+\frac{21\cdots 83}{44\cdots 09}$
| Monogenic: | Not computed | |
| Index: | $1$ | |
| Inessential primes: | None |
Class group and class number
| Ideal class group: | $C_{2}\times C_{4}\times C_{16}$, which has order $128$ (assuming GRH) |
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| Narrow class group: | $C_{2}\times C_{4}\times C_{16}$, which has order $128$ (assuming GRH) |
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Unit group
| Rank: | $9$ |
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| Torsion generator: |
\( -1 \)
(order $2$)
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| Fundamental units: |
$\frac{38\cdots 16}{34\cdots 93}a^{19}+\frac{12\cdots 46}{20\cdots 29}a^{18}-\frac{82\cdots 36}{34\cdots 93}a^{17}+\frac{36\cdots 43}{34\cdots 93}a^{16}-\frac{71\cdots 00}{34\cdots 93}a^{15}+\frac{27\cdots 36}{34\cdots 93}a^{14}-\frac{33\cdots 68}{34\cdots 93}a^{13}+\frac{10\cdots 34}{34\cdots 93}a^{12}-\frac{88\cdots 32}{34\cdots 93}a^{11}+\frac{22\cdots 64}{34\cdots 93}a^{10}-\frac{13\cdots 68}{34\cdots 93}a^{9}+\frac{20\cdots 96}{26\cdots 61}a^{8}-\frac{90\cdots 80}{26\cdots 61}a^{7}+\frac{17\cdots 38}{34\cdots 93}a^{6}-\frac{57\cdots 56}{34\cdots 93}a^{5}+\frac{71\cdots 44}{34\cdots 93}a^{4}-\frac{16\cdots 16}{34\cdots 93}a^{3}+\frac{16\cdots 28}{34\cdots 93}a^{2}-\frac{19\cdots 43}{34\cdots 93}a+\frac{48\cdots 47}{14\cdots 91}$, $\frac{96\cdots 48}{34\cdots 93}a^{19}-\frac{52\cdots 04}{34\cdots 93}a^{18}+\frac{20\cdots 90}{34\cdots 93}a^{17}-\frac{95\cdots 45}{34\cdots 93}a^{16}+\frac{18\cdots 28}{34\cdots 93}a^{15}-\frac{54\cdots 78}{26\cdots 61}a^{14}+\frac{84\cdots 48}{34\cdots 93}a^{13}-\frac{27\cdots 21}{34\cdots 93}a^{12}+\frac{22\cdots 16}{34\cdots 93}a^{11}-\frac{59\cdots 08}{34\cdots 93}a^{10}+\frac{34\cdots 33}{34\cdots 93}a^{9}-\frac{71\cdots 74}{34\cdots 93}a^{8}+\frac{30\cdots 36}{34\cdots 93}a^{7}-\frac{48\cdots 41}{34\cdots 93}a^{6}+\frac{11\cdots 22}{26\cdots 61}a^{5}-\frac{19\cdots 62}{34\cdots 93}a^{4}+\frac{38\cdots 55}{34\cdots 93}a^{3}-\frac{45\cdots 04}{34\cdots 93}a^{2}+\frac{44\cdots 55}{34\cdots 93}a-\frac{13\cdots 11}{14\cdots 91}$, $\frac{12\cdots 30}{44\cdots 09}a^{19}+\frac{88\cdots 58}{44\cdots 09}a^{18}-\frac{26\cdots 16}{44\cdots 09}a^{17}+\frac{96\cdots 54}{26\cdots 77}a^{16}-\frac{23\cdots 94}{44\cdots 09}a^{15}+\frac{12\cdots 69}{44\cdots 09}a^{14}-\frac{86\cdots 39}{34\cdots 93}a^{13}+\frac{29\cdots 49}{26\cdots 61}a^{12}-\frac{30\cdots 41}{44\cdots 09}a^{11}+\frac{11\cdots 52}{44\cdots 09}a^{10}-\frac{47\cdots 98}{44\cdots 09}a^{9}+\frac{13\cdots 60}{44\cdots 09}a^{8}-\frac{40\cdots 63}{44\cdots 09}a^{7}+\frac{50\cdots 52}{26\cdots 77}a^{6}-\frac{16\cdots 34}{44\cdots 09}a^{5}+\frac{24\cdots 97}{44\cdots 09}a^{4}-\frac{20\cdots 21}{34\cdots 93}a^{3}+\frac{21\cdots 60}{44\cdots 09}a^{2}-\frac{96\cdots 37}{44\cdots 09}a+\frac{16\cdots 57}{44\cdots 09}$, $\frac{84\cdots 92}{79\cdots 37}a^{19}-\frac{48\cdots 96}{79\cdots 37}a^{18}-\frac{12\cdots 32}{79\cdots 37}a^{17}-\frac{81\cdots 12}{61\cdots 49}a^{16}-\frac{54\cdots 72}{79\cdots 37}a^{15}-\frac{88\cdots 76}{79\cdots 37}a^{14}-\frac{32\cdots 16}{79\cdots 37}a^{13}-\frac{36\cdots 08}{79\cdots 37}a^{12}+\frac{44\cdots 28}{79\cdots 37}a^{11}-\frac{80\cdots 04}{79\cdots 37}a^{10}+\frac{13\cdots 64}{79\cdots 37}a^{9}-\frac{92\cdots 68}{79\cdots 37}a^{8}+\frac{14\cdots 16}{79\cdots 37}a^{7}-\frac{31\cdots 00}{46\cdots 61}a^{6}+\frac{78\cdots 60}{79\cdots 37}a^{5}-\frac{12\cdots 80}{61\cdots 49}a^{4}+\frac{23\cdots 04}{79\cdots 37}a^{3}-\frac{27\cdots 40}{79\cdots 37}a^{2}+\frac{24\cdots 64}{79\cdots 37}a-\frac{10\cdots 87}{79\cdots 37}$, $\frac{11\cdots 68}{22\cdots 45}a^{19}-\frac{29\cdots 83}{17\cdots 65}a^{18}+\frac{28\cdots 18}{22\cdots 45}a^{17}-\frac{65\cdots 27}{22\cdots 45}a^{16}+\frac{18\cdots 98}{22\cdots 45}a^{15}-\frac{89\cdots 34}{44\cdots 09}a^{14}+\frac{13\cdots 42}{22\cdots 45}a^{13}-\frac{15\cdots 58}{22\cdots 45}a^{12}+\frac{42\cdots 84}{22\cdots 45}a^{11}-\frac{28\cdots 69}{22\cdots 45}a^{10}+\frac{66\cdots 98}{22\cdots 45}a^{9}-\frac{17\cdots 34}{13\cdots 85}a^{8}+\frac{54\cdots 17}{22\cdots 45}a^{7}-\frac{16\cdots 28}{22\cdots 45}a^{6}+\frac{26\cdots 27}{22\cdots 45}a^{5}-\frac{10\cdots 04}{44\cdots 09}a^{4}+\frac{69\cdots 99}{22\cdots 45}a^{3}-\frac{77\cdots 89}{22\cdots 45}a^{2}+\frac{12\cdots 75}{44\cdots 09}a-\frac{24\cdots 37}{22\cdots 45}$, $\frac{10\cdots 59}{22\cdots 45}a^{19}+\frac{59\cdots 65}{44\cdots 09}a^{18}-\frac{19\cdots 06}{22\cdots 45}a^{17}+\frac{44\cdots 22}{22\cdots 45}a^{16}-\frac{15\cdots 09}{22\cdots 45}a^{15}+\frac{10\cdots 98}{97\cdots 15}a^{14}-\frac{60\cdots 88}{22\cdots 45}a^{13}+\frac{60\cdots 61}{22\cdots 45}a^{12}-\frac{12\cdots 41}{22\cdots 45}a^{11}+\frac{41\cdots 73}{22\cdots 45}a^{10}-\frac{60\cdots 82}{97\cdots 15}a^{9}-\frac{74\cdots 96}{22\cdots 45}a^{8}-\frac{12\cdots 70}{44\cdots 09}a^{7}-\frac{22\cdots 81}{44\cdots 09}a^{6}-\frac{47\cdots 99}{44\cdots 09}a^{5}-\frac{38\cdots 21}{22\cdots 45}a^{4}+\frac{14\cdots 30}{44\cdots 09}a^{3}-\frac{12\cdots 14}{22\cdots 45}a^{2}+\frac{15\cdots 29}{22\cdots 45}a-\frac{79\cdots 89}{22\cdots 45}$, $\frac{71\cdots 80}{34\cdots 93}a^{19}+\frac{23\cdots 52}{22\cdots 45}a^{18}-\frac{98\cdots 56}{22\cdots 45}a^{17}+\frac{18\cdots 26}{97\cdots 15}a^{16}-\frac{84\cdots 02}{22\cdots 45}a^{15}+\frac{30\cdots 84}{22\cdots 45}a^{14}-\frac{38\cdots 73}{22\cdots 45}a^{13}+\frac{22\cdots 25}{44\cdots 09}a^{12}-\frac{10\cdots 69}{22\cdots 45}a^{11}+\frac{47\cdots 27}{44\cdots 09}a^{10}-\frac{15\cdots 67}{22\cdots 45}a^{9}+\frac{27\cdots 83}{22\cdots 45}a^{8}-\frac{25\cdots 09}{44\cdots 09}a^{7}+\frac{17\cdots 54}{22\cdots 45}a^{6}-\frac{60\cdots 97}{22\cdots 45}a^{5}+\frac{50\cdots 28}{17\cdots 65}a^{4}-\frac{15\cdots 48}{22\cdots 45}a^{3}+\frac{14\cdots 33}{22\cdots 45}a^{2}-\frac{17\cdots 43}{22\cdots 45}a+\frac{93\cdots 87}{22\cdots 45}$, $\frac{30\cdots 64}{44\cdots 09}a^{19}-\frac{18\cdots 62}{22\cdots 45}a^{18}+\frac{20\cdots 88}{13\cdots 85}a^{17}-\frac{34\cdots 08}{22\cdots 45}a^{16}+\frac{32\cdots 22}{22\cdots 45}a^{15}-\frac{26\cdots 24}{22\cdots 45}a^{14}+\frac{90\cdots 69}{13\cdots 85}a^{13}-\frac{20\cdots 54}{44\cdots 09}a^{12}+\frac{40\cdots 79}{22\cdots 45}a^{11}-\frac{42\cdots 42}{44\cdots 09}a^{10}+\frac{60\cdots 87}{22\cdots 45}a^{9}-\frac{10\cdots 76}{97\cdots 15}a^{8}+\frac{96\cdots 75}{44\cdots 09}a^{7}-\frac{13\cdots 19}{22\cdots 45}a^{6}+\frac{16\cdots 69}{17\cdots 65}a^{5}-\frac{25\cdots 82}{13\cdots 85}a^{4}+\frac{59\cdots 18}{22\cdots 45}a^{3}-\frac{68\cdots 38}{22\cdots 45}a^{2}+\frac{33\cdots 04}{13\cdots 85}a-\frac{17\cdots 29}{17\cdots 65}$, $\frac{35\cdots 69}{22\cdots 45}a^{19}-\frac{24\cdots 94}{22\cdots 45}a^{18}-\frac{61\cdots 68}{22\cdots 45}a^{17}-\frac{98\cdots 47}{22\cdots 45}a^{16}-\frac{18\cdots 01}{10\cdots 45}a^{15}-\frac{10\cdots 16}{22\cdots 45}a^{14}-\frac{13\cdots 28}{22\cdots 45}a^{13}-\frac{55\cdots 21}{22\cdots 45}a^{12}-\frac{11\cdots 11}{13\cdots 85}a^{11}-\frac{28\cdots 33}{44\cdots 09}a^{10}-\frac{62\cdots 47}{34\cdots 93}a^{9}-\frac{19\cdots 18}{22\cdots 45}a^{8}+\frac{16\cdots 09}{22\cdots 45}a^{7}-\frac{23\cdots 84}{44\cdots 09}a^{6}+\frac{29\cdots 46}{44\cdots 09}a^{5}-\frac{38\cdots 02}{22\cdots 45}a^{4}+\frac{57\cdots 07}{22\cdots 45}a^{3}-\frac{73\cdots 73}{22\cdots 45}a^{2}+\frac{70\cdots 02}{22\cdots 45}a-\frac{13\cdots 33}{97\cdots 15}$
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| Regulator: | \( 1018200581271943.9 \) (assuming GRH) |
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Class number formula
\[ \begin{aligned}\lim_{s\to 1} (s-1)\zeta_K(s) =\mathstrut & \frac{2^{r_1}\cdot (2\pi)^{r_2}\cdot R\cdot h}{w\cdot\sqrt{|D|}}\cr \approx\mathstrut &\frac{2^{0}\cdot(2\pi)^{10}\cdot 1018200581271943.9 \cdot 128}{2\cdot\sqrt{5117380860656444079832785566505699574289404854272}}\cr\approx \mathstrut & 2.76240993920227 \end{aligned}\] (assuming GRH)
Galois group
$C_{20}:C_4$ (as 20T18):
| A solvable group of order 80 |
| The 14 conjugacy class representatives for $C_{20}:C_4$ |
| Character table for $C_{20}:C_4$ |
Intermediate fields
| \(\Q(\sqrt{1001}) \), \(\Q(\sqrt{-77 +2 \sqrt{1001}})\), 5.1.35152.1, deg 10 |
Fields in the database are given up to isomorphism. Isomorphic intermediate fields are shown with their multiplicities.
Sibling fields
| Degree 20 sibling: | data not computed |
| Degree 40 siblings: | data not computed |
| Minimal sibling: | 20.0.393644681588957236910214274346592274945338834944.1 |
Frobenius cycle types
| $p$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | $31$ | $37$ | $41$ | $43$ | $47$ | $53$ | $59$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cycle type | R | $20$ | ${\href{/padicField/5.4.0.1}{4} }^{4}{,}\,{\href{/padicField/5.2.0.1}{2} }{,}\,{\href{/padicField/5.1.0.1}{1} }^{2}$ | R | R | R | ${\href{/padicField/17.2.0.1}{2} }^{10}$ | ${\href{/padicField/19.4.0.1}{4} }^{4}{,}\,{\href{/padicField/19.2.0.1}{2} }^{2}$ | ${\href{/padicField/23.2.0.1}{2} }^{10}$ | $20$ | ${\href{/padicField/31.4.0.1}{4} }^{4}{,}\,{\href{/padicField/31.2.0.1}{2} }{,}\,{\href{/padicField/31.1.0.1}{1} }^{2}$ | ${\href{/padicField/37.4.0.1}{4} }^{4}{,}\,{\href{/padicField/37.2.0.1}{2} }^{2}$ | ${\href{/padicField/41.4.0.1}{4} }^{4}{,}\,{\href{/padicField/41.2.0.1}{2} }^{2}$ | ${\href{/padicField/43.4.0.1}{4} }^{5}$ | ${\href{/padicField/47.4.0.1}{4} }^{4}{,}\,{\href{/padicField/47.2.0.1}{2} }{,}\,{\href{/padicField/47.1.0.1}{1} }^{2}$ | ${\href{/padicField/53.5.0.1}{5} }^{4}$ | ${\href{/padicField/59.4.0.1}{4} }^{4}{,}\,{\href{/padicField/59.2.0.1}{2} }{,}\,{\href{/padicField/59.1.0.1}{1} }^{2}$ |
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 |
|---|---|---|---|---|---|---|---|
|
\(2\)
| 2.5.4.1 | $x^{5} + 2$ | $5$ | $1$ | $4$ | $F_5$ | $$[\ ]_{5}^{4}$$ |
| 2.5.4.1 | $x^{5} + 2$ | $5$ | $1$ | $4$ | $F_5$ | $$[\ ]_{5}^{4}$$ | |
| 2.10.8.1 | $x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 3$ | $5$ | $2$ | $8$ | $F_5$ | $$[\ ]_{5}^{4}$$ | |
|
\(7\)
| 7.4.3.1 | $x^{4} + 7$ | $4$ | $1$ | $3$ | $D_{4}$ | $$[\ ]_{4}^{2}$$ |
| 7.16.12.1 | $x^{16} + 20 x^{14} + 16 x^{13} + 162 x^{12} + 240 x^{11} + 776 x^{10} + 1344 x^{9} + 2539 x^{8} + 3696 x^{7} + 5016 x^{6} + 5312 x^{5} + 4594 x^{4} + 2928 x^{3} + 1404 x^{2} + 432 x + 88$ | $4$ | $4$ | $12$ | $C_4:C_4$ | $$[\ ]_{4}^{4}$$ | |
|
\(11\)
| 11.4.3.2 | $x^{4} + 22$ | $4$ | $1$ | $3$ | $D_{4}$ | $$[\ ]_{4}^{2}$$ |
| 11.16.12.1 | $x^{16} + 32 x^{14} + 40 x^{13} + 392 x^{12} + 960 x^{11} + 2840 x^{10} + 7920 x^{9} + 15256 x^{8} + 28320 x^{7} + 45280 x^{6} + 47840 x^{5} + 30768 x^{4} + 11840 x^{3} + 2656 x^{2} + 320 x + 27$ | $4$ | $4$ | $12$ | $C_4:C_4$ | $$[\ ]_{4}^{4}$$ | |
|
\(13\)
| 13.2.1.1 | $x^{2} + 13$ | $2$ | $1$ | $1$ | $C_2$ | $$[\ ]_{2}$$ |
| 13.2.1.1 | $x^{2} + 13$ | $2$ | $1$ | $1$ | $C_2$ | $$[\ ]_{2}$$ | |
| 13.4.3.2 | $x^{4} + 13$ | $4$ | $1$ | $3$ | $C_4$ | $$[\ ]_{4}$$ | |
| 13.4.3.2 | $x^{4} + 13$ | $4$ | $1$ | $3$ | $C_4$ | $$[\ ]_{4}$$ | |
| 13.4.3.2 | $x^{4} + 13$ | $4$ | $1$ | $3$ | $C_4$ | $$[\ ]_{4}$$ | |
| 13.4.3.2 | $x^{4} + 13$ | $4$ | $1$ | $3$ | $C_4$ | $$[\ ]_{4}$$ |