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Properties

Label 2.1.4.10a1.3-1.4.26a
Base 2.1.4.10a1.3
Degree \(4\)
e \(4\)
f \(1\)
c \(26\)

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Defining polynomial

$x^{4} + \left(b_{27} \pi^{7} + a_{23} \pi^{6}\right) x^{3} + \left(b_{30} \pi^{8} + b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5}\right) x^{2} + \left(b_{29} \pi^{8} + b_{25} \pi^{7}\right) x + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.10a1.3
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $26$
Absolute Artin slopes: $[3,\frac{7}{2},\frac{14}{3},\frac{14}{3}]$
Swan slopes: $[\frac{23}{3},\frac{23}{3}]$
Means: $\langle\frac{23}{6},\frac{23}{4}\rangle$
Rams: $(\frac{23}{3},\frac{23}{3})$
Field count: $64$ (complete)
Ambiguity: $1$
Mass: $128$
Absolute Mass: $64$

Diagrams

Varying

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

Galois group: $C_2^6.(D_4\times S_4)$ (incomplete)
Hidden Artin slopes: not computed (show 52), $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ (show 12) (incomplete)
Indices of inseparability: $[51,44,28,16,0]$
Associated inertia: $[1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 64

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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
2.1.16.66c1.129 $x^{16} + 4 x^{12} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.130 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.131 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.132 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.133 $x^{16} + 4 x^{12} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.134 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.135 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.136 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.137 $x^{16} + 4 x^{12} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.138 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.139 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.140 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.141 $x^{16} + 4 x^{12} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.142 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.143 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.144 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.145 $x^{16} + 4 x^{12} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.146 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.147 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.148 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.149 $x^{16} + 4 x^{12} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.150 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.151 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.152 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.153 $x^{16} + 4 x^{12} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.154 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.155 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.156 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.157 $x^{16} + 4 x^{12} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.158 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.159 $x^{16} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.160 $x^{16} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ $[2, \frac{8}{3}, \frac{8}{3}, 3, \frac{7}{2}, \frac{23}{6}, \frac{23}{6}, \frac{49}{12}, \frac{49}{12}, \frac{14}{3}, \frac{14}{3}]_{3}^{2}$ $[1,\frac{5}{3},\frac{5}{3},2,\frac{5}{2},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12},\frac{11}{3},\frac{11}{3}]_{3}^{2}$ $[2,\frac{8}{3},\frac{8}{3},\frac{23}{6},\frac{23}{6},\frac{49}{12},\frac{49}{12}]^{2}_{3}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{6},\frac{17}{6},\frac{37}{12},\frac{37}{12}]^{2}_{3}$ $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.161 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.162 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.163 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.164 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.165 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.166 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.167 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.168 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.169 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.170 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.171 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.172 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.173 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.174 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.175 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.176 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{6} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.177 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.66c1.178 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{10} + 16 x^{5} + 16 x^{3} + 10$ $C_2^6.(D_4\times S_4)$ (as 16T1756) $12288$ $1$ not computed not computed not computed not computed $[51, 44, 28, 16, 0]$ $[1, 1, 1]$ $z^8 + 1,z^4 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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