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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
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Results (16 matches)

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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.1.16.42k1.22 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.23 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.24 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.31 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.32 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.33 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.34 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.40 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 9, 25, 41]$
2.1.16.42k1.63 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.64 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.70 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.71 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.72 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.74 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.79 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.80 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2^4.\SD_{16}$ (as 16T673) $4$ $1$ $[2, 2, \frac{5}{2}, \frac{13}{4}]$ $[1,1,\frac{3}{2},\frac{9}{4}]$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $t + 1$ $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
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