Properties

Label 2.1.4.11a1.19-1.4.28a
Base 2.1.4.11a1.19
Degree \(4\)
e \(4\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{4} + \left(b_{39} \pi^{10} + b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{37} \pi^{10} + b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{40} \pi^{11} + c_{20} \pi^{6} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.11a1.19
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Absolute Artin slopes: $[3,4,\frac{17}{4},\frac{11}{2}]$
Swan slopes: $[5,10]$
Means: $\langle\frac{5}{2},\frac{25}{4}\rangle$
Rams: $(5,15)$
Field count: $512$ (complete)
Ambiguity: $4$
Mass: $512$
Absolute Mass: $256$

Diagrams

Varying

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

Indices of inseparability: $[57,42,32,16,0]$
Associated inertia: $[1,1,1,1]$
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 512

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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
2.1.16.72c1.6209 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6210 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6211 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6212 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6213 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6214 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6215 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6216 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6217 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6218 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6219 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6220 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6221 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6222 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6223 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6224 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6225 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6226 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6227 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6228 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6229 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6230 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6231 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6232 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6233 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6234 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6235 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6236 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6237 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6238 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6239 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6240 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6241 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6242 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6243 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6244 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6245 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6246 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6247 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6248 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 32 x^{3} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6249 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6250 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6251 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6252 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6253 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6254 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6255 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6256 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{5} + 16 x^{4} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6257 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 4 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.72c1.6258 $x^{16} + 16 x^{15} + 8 x^{14} + 8 x^{10} + 16 x^{9} + 36 x^{8} + 32 x^{7} + 32 x^{5} + 16 x^{2} + 32 x + 26$ $C_2^7.C_2\wr C_2^2$ (as 16T1706) $8192$ $2$ not computed not computed not computed not computed $[57, 42, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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