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Properties

Label 2.1.8.31a1.149-1.2.17a
Base 2.1.8.31a1.149
Degree \(2\)
e \(2\)
f \(1\)
c \(17\)

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Defining polynomial

$x^{2} + \left(b_{31} \pi^{16} + b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9}\right) x + c_{32} \pi^{17} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.8.31a1.149
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $17$
Absolute Artin slopes: $[3,4,5,6]$
Swan slopes: $[16]$
Means: $\langle8\rangle$
Rams: $(16)$
Field count: $136$ (complete)
Ambiguity: $2$
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: $C_{16}:C_4$ (show 4), $C_8.\OD_{16}$ (show 4), $C_4^2.\OD_{16}$ (show 8), $C_2^5.\OD_{16}$ (show 8), $C_2^6.\OD_{16}$ (show 16), $C_2^7.\OD_{16}$ (show 32), $C_2\wr \OD_{16}$ (show 64) (incomplete)
Hidden Artin slopes: not computed (show 112), $[2,\frac{7}{2},\frac{17}{4}]^{2}$ (show 8), $[\ ]^{4}$ (show 2), $[2]^{2}$ (show 2), $[2,\frac{7}{2}]^{2}$ (show 4), $[2,\frac{7}{2},\frac{17}{4},\frac{19}{4}]^{2}$ (show 8) (incomplete)
Indices of inseparability: $[64,48,32,16,0]$
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 136

Next   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
2.1.16.79a1.34681 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34682 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 66$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34683 $x^{16} + 32 x^{15} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34684 $x^{16} + 32 x^{15} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 66$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34685 $x^{16} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34686 $x^{16} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 66$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34687 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34688 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 66$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34689 $x^{16} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34690 $x^{16} + 32 x^{15} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34691 $x^{16} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34692 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34693 $x^{16} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34694 $x^{16} + 32 x^{15} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34695 $x^{16} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34696 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34697 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34698 $x^{16} + 32 x^{15} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34699 $x^{16} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34700 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34701 $x^{16} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34702 $x^{16} + 32 x^{15} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34703 $x^{16} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34704 $x^{16} + 32 x^{15} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34705 $x^{16} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34706 $x^{16} + 32 x^{15} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34707 $x^{16} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34708 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34709 $x^{16} + 32 x^{11} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34710 $x^{16} + 32 x^{15} + 32 x^{11} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34711 $x^{16} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34712 $x^{16} + 32 x^{15} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 32 x^{9} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 2$ $C_2^7.\OD_{16}$ (as 16T1405) $2048$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34713 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34714 $x^{16} + 32 x^{15} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34715 $x^{16} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34716 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34717 $x^{16} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34718 $x^{16} + 32 x^{15} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34719 $x^{16} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34720 $x^{16} + 32 x^{15} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34721 $x^{16} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34722 $x^{16} + 32 x^{15} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34723 $x^{16} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34724 $x^{16} + 32 x^{15} + 32 x^{13} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34725 $x^{16} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34726 $x^{16} + 32 x^{15} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34727 $x^{16} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34728 $x^{16} + 32 x^{15} + 32 x^{13} + 32 x^{11} + 16 x^{10} + 4 x^{8} + 32 x^{7} + 16 x^{6} + 32 x^{3} + 2$ $C_2^6.\OD_{16}$ (as 16T1200) $1024$ $2$ not computed not computed not computed not computed $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34729 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 32 x^{3} + 2$ $C_4^2.\OD_{16}$ (as 16T629) $256$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5, 6]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},4,5]^{2}$ $[2,\frac{7}{2},\frac{17}{4}]^{2}$ $[1,\frac{5}{2},\frac{13}{4}]^{2}$ $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.79a1.34730 $x^{16} + 16 x^{10} + 4 x^{8} + 16 x^{6} + 32 x^{5} + 32 x^{3} + 66$ $C_4^2.\OD_{16}$ (as 16T629) $256$ $4$ $[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5, 6]^{2}$ $[1,2,\frac{5}{2},3,\frac{13}{4},4,5]^{2}$ $[2,\frac{7}{2},\frac{17}{4}]^{2}$ $[1,\frac{5}{2},\frac{13}{4}]^{2}$ $[64, 48, 32, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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