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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
2.1.16.56l1.65 $x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.66 $x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.67 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.68 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.69 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.70 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.71 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.72 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.109 $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.110 $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.111 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.112 $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.113 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.114 $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.115 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
2.1.16.56l1.116 $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $2$ $1$ $16$ $56$ $C_2^4.D_8$ (as 16T705) $4$ $1$ $[2, 3, 4, 4]$ $[1,2,3,3]$ $[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$ $[1,2,2,\frac{5}{2},3,3]^{4}$ $[3,\frac{7}{2}]^{4}$ $[2,\frac{5}{2}]^{4}$ $t + 1$ $x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$ $[41, 36, 20, 8, 0]$ $[1, 1, 2]$ $z^8 + 1,z^4 + 1,z^3 + 1$ $[1, 7, 15, 31, 47]$
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