Properties

Label 2.1.4.8b1.6-1.4.26c
Base 2.1.4.8b1.6
Degree \(4\)
e \(4\)
f \(1\)
c \(26\)

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Defining polynomial

$x^{4} + \left(b_{31} \pi^{8} + b_{27} \pi^{7} + a_{23} \pi^{6}\right) x^{3} + \left(b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5} + a_{14} \pi^{4}\right) x^{2} + \left(b_{29} \pi^{8} + b_{25} \pi^{7}\right) x + c_{32} \pi^{9} + c_{28} \pi^{8} + \pi$

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 $c$: $26$
Absolute Artin slopes: $[2,3,4,\frac{17}{4}]$
Swan slopes: $[7,8]$
Means: $\langle\frac{7}{2},\frac{23}{4}\rangle$
Rams: $(7,9)$
Field count: $112$ (complete)
Ambiguity: $4$
Mass: $128$
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: $C_2^4:C_4$ (show 4), $C_2^4:C_4$ (show 4), $C_2^3.C_2^3$ (show 4), $C_2^3.C_2^3$ (show 4), $C_2\wr C_2^2$ (show 8), $C_2\wr C_2^2$ (show 16), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 4), $C_2^4:Q_8$ (show 8), $C_2^4:Q_8$ (show 8), $C_2^4:D_4$ (show 8), $C_2^4:Q_8$ (show 4), $C_2^4:Q_8$ (show 4), $C_2^4:D_4$ (show 8), $C_2^4.C_2^3$ (show 8)
Hidden Artin slopes: $[\frac{7}{2}]^{2}$ (show 40), $[3,\frac{7}{2}]^{2}$ (show 48), $[2,\frac{7}{2}]^{2}$ (show 24)
Indices of inseparability: $[43,34,20,8,0]$
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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Showing 1-50 of 112

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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
2.1.16.58n1.721 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.722 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.723 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 14$ $C_2^3.C_2^3$ (as 16T112) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.724 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^4:C_4$ (as 16T94) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.725 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^3.C_2^3$ (as 16T112) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.726 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4:C_4$ (as 16T94) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.727 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 14$ $C_2^4:C_4$ (as 16T94) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.728 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^3.C_2^3$ (as 16T112) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.729 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2^4:C_4$ (as 16T94) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.730 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^3.C_2^3$ (as 16T112) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.731 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.732 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4.D_4$ (as 16T318) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.733 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.734 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.735 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2\wr C_2^2$ (as 16T128) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.736 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2\wr C_2^2$ (as 16T128) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.737 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.738 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.739 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.740 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.741 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.742 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.743 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.744 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.745 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.746 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4:D_4$ (as 16T350) $128$ $4$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.747 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 14$ $C_2\wr C_2^2$ (as 16T128) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.748 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 14$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.749 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 14$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.750 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.751 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 14$ $C_2\wr C_2^2$ (as 16T149) $64$ $8$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.752 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2\wr C_2^2$ (as 16T128) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.753 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.754 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.755 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.756 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.757 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.758 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.C_2^3$ (as 16T383) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.759 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.760 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4:Q_8$ (as 16T368) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.761 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T347) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.762 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T347) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.763 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T347) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.764 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 30$ $C_2^4:Q_8$ (as 16T347) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.765 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.766 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.767 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.768 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.769 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.58n1.770 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $C_2^4.D_4$ (as 16T208) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[43, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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