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Properties

Label 2.1.16.68f
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(68\)

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Defining polynomial

$x^{16} + 16 b_{63} x^{15} + 8 b_{46} x^{14} + 16 b_{61} x^{13} + 4 a_{28} x^{12} + 16 b_{59} x^{11} + 8 a_{42} x^{10} + 16 b_{57} x^{9} + \left(4 b_{24} + 8 c_{40} + 16 c_{56}\right) x^{8} + 16 b_{55} x^{7} + 16 b_{54} x^{6} + 16 a_{53} x^{5} + 8 b_{36} x^{4} + 16 b_{50} x^{2} + 8 c_{32} + 32 c_{64} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $68$
Artin slopes: $[3,\frac{7}{2},\frac{9}{2},5]$
Swan slopes: $[2,\frac{5}{2},\frac{7}{2},4]$
Means: $\langle1,\frac{7}{4},\frac{21}{8},\frac{53}{16}\rangle$
Rams: $(2,3,7,11)$
Field count: $2048$ (complete)
Ambiguity: $16$
Mass: $1024$
Absolute Mass: $1024$

Diagrams

Varying

Indices of inseparability: $[53,42,28,16,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,3,7,15,31]$

Galois groups and Hidden Artin slopes

Note that the following data has not all been computed for fields in this family, so the table below is incomplete.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
Sort order Select

Showing 1-50 of at least 1000

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Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.1.16.68f1.1 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.2 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.3 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.4 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.5 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.6 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.7 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.8 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.9 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.10 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.11 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.12 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.13 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.14 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.15 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.16 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.17 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.18 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.19 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.20 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.21 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.22 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.23 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.24 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.25 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.26 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.27 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.28 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.29 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.30 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.31 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.32 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.33 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.34 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.35 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.36 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.37 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.38 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.39 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.40 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.41 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.42 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.43 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.44 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.45 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.46 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.47 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.48 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.49 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.50 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 2$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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