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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
2.1.16.42b1.41 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.42 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 2$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.43 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 2$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.50 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 2$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.51 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 2$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.52 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 2$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.61 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.64 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 2$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.113 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 6$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.114 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 6$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.119 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 6$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.120 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 6$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.129 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 6$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.130 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 6$ $2$ $1$ $16$ $42$ $D_4\times A_4$ (as 16T179) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.135 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 6$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.136 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 6$ $2$ $1$ $16$ $42$ $D_4.A_4$ (as 16T180) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,\frac{5}{2}]^{3}$ $[3]^{3}$ $[2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
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