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Properties

Label 2.1.4.10a1.3-1.4.20d
Base 2.1.4.10a1.3
Degree \(4\)
e \(4\)
f \(1\)
c \(20\)

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Defining polynomial

$x^{4} + \left(b_{23} \pi^{6} + b_{19} \pi^{5}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{21} \pi^{6} + a_{17} \pi^{5}\right) x + c_{24} \pi^{7} + c_{20} \pi^{6} + \pi$

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 $c$: $20$
Absolute Artin slopes: $[3,\frac{7}{2},4,\frac{17}{4}]$
Swan slopes: $[5,6]$
Means: $\langle\frac{5}{2},\frac{17}{4}\rangle$
Rams: $(5,7)$
Field count: $40$ (complete)
Ambiguity: $4$
Mass: $32$
Absolute Mass: $16$

Diagrams

Varying

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

Galois group: $C_2^3:C_4$ (show 4), $C_2^4:C_4$ (show 4), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 8), $C_2^4.C_2^3$ (show 4), $C_4^2:D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_2\wr D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_2^4.(C_4\times D_4)$ (show 8)
Hidden Artin slopes: $[2,2]^{2}$ (show 12), $[2,3]^{2}$ (show 12), $[2]$ (show 4), $[2,2,3]^{4}$ (show 8), $[2]^{2}$ (show 4)
Indices of inseparability: $[45,38,28,16,0]$
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 all 40

  displayed columns for results
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
2.1.16.60o1.81 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 10$ $C_2^4.D_4$ (as 16T224) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.82 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 26$ $C_2^4.D_4$ (as 16T224) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.83 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 10$ $C_2^4.C_2^3$ (as 16T286) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.84 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x + 10$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.85 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 16 x + 10$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.86 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 26$ $C_2^4.C_2^3$ (as 16T286) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.87 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x + 26$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.88 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 16 x + 26$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.89 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 10$ $C_2^3:C_4$ (as 16T52) $32$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[2]$ $[1]$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.90 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 10$ $C_2^3:C_4$ (as 16T52) $32$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[2]$ $[1]$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.91 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 26$ $C_2^3:C_4$ (as 16T52) $32$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[2]$ $[1]$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.92 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 26$ $C_2^3:C_4$ (as 16T52) $32$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]$ $[1,2,\frac{5}{2},3,\frac{13}{4}]$ $[2]$ $[1]$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.93 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 10$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.94 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 10$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.95 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x + 10$ $C_2^4.C_2^3$ (as 16T286) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.96 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 26$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.97 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x^{4} + 26$ $C_2^4.D_4$ (as 16T247) $128$ $4$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.98 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{6} + 16 x + 26$ $C_2^4.C_2^3$ (as 16T286) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.99 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.100 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.101 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$ $C_4^2:D_4$ (as 16T341) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.102 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 10$ $C_4^2:D_4$ (as 16T341) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.103 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x + 10$ $C_4^2:D_4$ (as 16T365) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.104 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 16 x + 10$ $C_4^2:D_4$ (as 16T365) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.105 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.106 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.107 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$ $C_2\wr D_4$ (as 16T395) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.108 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 10$ $C_2\wr D_4$ (as 16T395) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.109 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x + 10$ $C_4^2:D_4$ (as 16T399) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.110 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{4} + 16 x + 10$ $C_4^2:D_4$ (as 16T399) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.151 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.152 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{8} + 8 x^{6} + 24 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.153 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.154 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{8} + 8 x^{6} + 24 x^{4} + 10$ $C_2^4.(C_4\times D_4)$ (as 16T867) $512$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, \frac{17}{4}]^{4}$ $[1,1,2,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.155 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 10$ $C_2^4:C_4$ (as 16T93) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2]^{2}$ $[1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.156 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 24 x^{4} + 10$ $C_2^4:C_4$ (as 16T93) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2]^{2}$ $[1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.157 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 26$ $C_2^4:C_4$ (as 16T93) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2]^{2}$ $[1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.158 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 24 x^{4} + 26$ $C_2^4:C_4$ (as 16T93) $64$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2]^{2}$ $[1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.159 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 10$ $C_2^4.D_4$ (as 16T224) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.60o1.160 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 26$ $C_2^4.D_4$ (as 16T224) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, \frac{17}{4}]^{2}$ $[1,1,2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[2,2]^{2}$ $[1,1]^{2}$ $[45, 38, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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