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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
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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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
2.1.16.56l1.7 $x^{16} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 9, 29, 45, 61]$
2.1.16.56l1.10 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 9, 29, 45, 61]$
2.1.16.56l1.21 $x^{16} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 9, 29, 45, 61]$
2.1.16.56l1.24 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 9, 29, 45, 61]$
2.1.16.56l1.40 $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.41 $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.54 $x^{16} + 8 x^{15} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.55 $x^{16} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{14} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 10$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 32, 48]$
2.1.16.56l1.199 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 6$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 6$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.200 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 6$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 6$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.223 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.224 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 6$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.229 $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 14$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 14$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.234 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 14$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 14$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.255 $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 14$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 14$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
2.1.16.56l1.256 $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 14$ $2$ $1$ $16$ $56$ $C_2^4.C_2^3$ (as 16T229) $2$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{2}$ $[1,2,2,\frac{5}{2},3,3]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $t + 1$ $x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 14$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 2, 4, 8, 32]$
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