$p$-adic family 2.2.4.22a1.48-1.2.8a

• Label: 2.2.4.22a1.48-1.2.8a
• Base: 2.2.4.22a1.48
• Degree: \(2\)
• e: \(2\)
• f: \(1\)
• c: \(8\)

Defining polynomial

$x^{2} + \left(b_{13} \pi^{7} + b_{11} \pi^{6} + b_{9} \pi^{5} + a_{7} \pi^{4}\right) x + c_{14} \pi^{8} + \pi$

Invariants

Residue field characteristic:	$2$
Degree:	$2$
Base field:	2.2.4.22a1.48
Ramification index $e$:	$2$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$8$
Absolute Artin slopes:	$[3,4,\frac{19}{4}]$
Swan slopes:	$[7]$
Means:	$\langle\frac{7}{2}\rangle$
Rams:	$(7)$
Field count:	$192$ (complete)
Ambiguity:	$2$
Mass:	$192$
Absolute Mass:	$96$

Diagrams

Varying

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

Galois group:	$C_2^6.C_2\wr C_4$ (show 64), $C_2^7.C_2\wr C_4$ (show 64), $C_2^7.C_2\wr C_4$ (show 64) (incomplete)
Hidden Artin slopes:	not computed (show 160), $[2,2,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ (show 32) (incomplete)
Indices of inseparability:	$[23,16,8,0]$
Associated inertia:	$[1,1,1]$
Jump Set:	$[1,3,7,15]$

Fields

Showing 1-50 of 192

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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
2.2.8.60a1.1953	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1954	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1955	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1956	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1957	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1958	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1959	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1960	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1961	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1962	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1963	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1964	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1965	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1966	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1967	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1968	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1969	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1970	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1971	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1972	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1973	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1974	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1975	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1976	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1977	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1978	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1979	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1980	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1981	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1982	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1983	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1984	$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1985	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1986	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1987	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1988	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1989	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1990	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1991	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1992	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1993	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1994	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1995	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1996	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1997	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1998	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.1999	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.2000	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.2001	$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.2.8.60a1.2002	$( x^{2} + x + 1 )^{8} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$	$C_2^7.C_2\wr C_4$ (as 16T1718)	$8192$	$2$	not computed	not computed	not computed	not computed	$[23, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$

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