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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
2.1.16.42b1.13 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.14 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.15 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.16 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.33 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.34 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.35 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{3} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.36 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{3} + 8 x + 2$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.42b1.81 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.82 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.91 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.92 $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.102 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x + 6$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{7} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.103 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x + 6$ $2$ $1$ $16$ $42$ $(C_2^2\times C_4):A_4$ (as 16T426) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.110 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.42b1.111 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $2$ $1$ $16$ $42$ $C_2\wr A_4$ (as 16T427) $3$ $1$ $[2, 2, 2, \frac{7}{2}]$ $[1,1,1,\frac{5}{2}]$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[3,3]^{3}$ $[2,2]^{3}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 8 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $[27, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
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