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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
2.1.16.54o1.142 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 28, 44]$
2.1.16.54o1.143 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 18$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 18$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 32, 48, 64]$
2.1.16.54o1.151 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 2$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 28, 44]$
2.1.16.54o1.152 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 18$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 18$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 32, 48, 64]$
2.1.16.54o1.201 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.54o1.202 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 26$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 26$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.54o1.212 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 10$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.54o1.213 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 26$ $2$ $1$ $16$ $54$ $C_2^2 : C_4$ (as 16T10) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 26$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 7, 14, 32, 48]$
2.1.16.54o1.236 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.237 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.247 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.248 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.297 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.298 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.306 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.307 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $2$ $1$ $16$ $54$ $C_4:C_4$ (as 16T8) $1$ $1$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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