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Properties

Label 2.1.8.12b1.3-1.2.14a
Base 2.1.8.12b1.3
Degree \(2\)
e \(2\)
f \(1\)
c \(14\)

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Defining polynomial

$x^{2} + \left(b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + b_{15} \pi^{8} + a_{13} \pi^{7}\right) x + c_{26} \pi^{14} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.8.12b1.3
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $14$
Absolute Artin slopes: $[\frac{4}{3},\frac{4}{3},2,\frac{13}{4}]$
Swan slopes: $[13]$
Means: $\langle\frac{13}{2}\rangle$
Rams: $(13)$
Field count: $80$ (complete)
Ambiguity: $2$
Mass: $64$
Absolute Mass: $32$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_2^5:S_4$ (show 8), $C_2^5:S_4$ (show 16), $(C_2^3\times C_4):S_4$ (show 16), $(C_2^3\times C_4):S_4$ (show 8), $C_2^5:\GL(2,3)$ (show 32) (incomplete)
Hidden Artin slopes: not computed (show 32), $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ (show 48) (incomplete)
Indices of inseparability: $[23,10,4,4,0]$
Associated inertia: $[1,1,1]$
Jump Set: $[1,2,5,21,37]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 80

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Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.1.16.38h1.161 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.162 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.163 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.164 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.165 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.166 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.167 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.168 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.169 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $(C_2^3\times C_4):S_4$ (as 16T1057) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.170 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 8 x + 2$ $(C_2^3\times C_4):S_4$ (as 16T1057) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.171 $x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.172 $x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.173 $x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.174 $x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.175 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.176 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.177 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.178 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 2$ $(C_2^3\times C_4):S_4$ (as 16T1046) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.179 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $(C_2^3\times C_4):S_4$ (as 16T1057) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.180 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 8 x + 2$ $(C_2^3\times C_4):S_4$ (as 16T1057) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.181 $x^{16} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.182 $x^{16} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.183 $x^{16} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.184 $x^{16} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.185 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.186 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.187 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.188 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.189 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.190 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.191 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.192 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.193 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.194 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.195 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.196 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.197 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.198 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.199 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.200 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 8 x + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.201 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.202 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.203 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.204 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 2$ $C_2^5:S_4$ (as 16T1045) $768$ $4$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.205 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.206 $x^{16} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 8 x + 2$ $C_2^5:S_4$ (as 16T1044) $768$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, \frac{13}{4}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},\frac{9}{4}]_{3}^{2}$ $[3,\frac{19}{6},\frac{19}{6}]^{2}_{3}$ $[2,\frac{13}{6},\frac{13}{6}]^{2}_{3}$ $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.207 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.208 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 10 x^{4} + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.209 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
2.1.16.38h1.210 $x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 10 x^{4} + 8 x + 2$ $C_2^5:\GL(2,3)$ (as 16T1316) $1536$ $2$ not computed not computed not computed not computed $[23, 10, 4, 4, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 5, 21, 37]$
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