Properties

Label 2.1.4.8b1.6-1.4.28b
Base 2.1.4.8b1.6
Degree \(4\)
e \(4\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{4} + \left(b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5} + a_{14} \pi^{4}\right) x^{2} + \left(b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{36} \pi^{10} + c_{28} \pi^{8} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.8b1.6
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Absolute Artin slopes: $[2,3,4,\frac{9}{2}]$
Swan slopes: $[7,9]$
Means: $\langle\frac{7}{2},\frac{25}{4}\rangle$
Rams: $(7,11)$
Field count: $128$ (complete)
Ambiguity: $4$
Mass: $256$
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: $C_2^5.(C_2\times D_4)$ (show 16), $C_2^3\wr C_2:C_4$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16), $C_2^4.(C_4\times D_4)$ (show 16), $C_2^6.Q_8$ (show 16), $(C_2^2\times C_4^2):Q_8$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16), $(D_4\times C_2^3).C_2^3$ (show 16)
Hidden Artin slopes: $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$
Indices of inseparability: $[45,34,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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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
2.1.16.60l1.897 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.898 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.899 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.900 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.901 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.902 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.903 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.904 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.905 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.906 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.907 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.908 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.909 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.910 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.911 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.912 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.913 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.914 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.915 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.916 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.917 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.918 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.919 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.920 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.921 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times C_4^2):Q_8$ (as 16T1008) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.922 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.923 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.924 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.925 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.926 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.927 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.928 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 30$ $C_2^5.(C_2\times D_4)$ (as 16T813) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.929 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.930 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.931 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.932 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.933 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.934 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.935 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.936 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(D_4\times C_2^3).C_2^3$ (as 16T853) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.937 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.938 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.939 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.940 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.941 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.942 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.943 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.944 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.945 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.946 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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