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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
Ramification index Discriminant exponent Inertia subgroup Galois tame degree Indices
Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (7 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
2.8.12.16 $x^{8} + 8 x^{7} + 32 x^{6} + 78 x^{5} + 137 x^{4} + 186 x^{3} + 128 x^{2} - 10 x + 7$ $2$ $4$ $2$ $12$ $A_4\times C_2$ (as 8T13) $6$ $1$ $[2, 2]$ $[2, 2]^{6}$ $t^{2} + t + 1$ $x^{4} + 2 x^{3} + 2 x^{2} + 6$ $[3, 2, 0]$ $[3]$
2.8.14.1 $x^{8} + 2 x^{7} + 6$ $2$ $8$ $1$ $14$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 2]$ $[2, 2, 2]^{3}$ $t + 1$ $x^{8} + 2 x^{7} + 6$ $[7, 7, 7, 0]$ $[3]$
2.8.14.2 $x^{8} + 2 x^{7} + 2$ $2$ $8$ $1$ $14$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 2]$ $[2, 2, 2]^{3}$ $t + 1$ $x^{8} + 2 x^{7} + 2$ $[7, 7, 7, 0]$ $[3]$
2.8.18.57 $x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10$ $2$ $8$ $1$ $18$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 3]$ $[2, 2, 3]^{3}$ $t + 1$ $x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10$ $[11, 6, 4, 0]$ $[1, 3]$
2.8.18.58 $x^{8} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 10$ $2$ $8$ $1$ $18$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 3]$ $[2, 2, 3]^{3}$ $t + 1$ $x^{8} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 10$ $[11, 6, 4, 0]$ $[1, 3]$
2.8.18.59 $x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 2$ $2$ $8$ $1$ $18$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 3]$ $[2, 2, 3]^{3}$ $t + 1$ $x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 2$ $[11, 6, 4, 0]$ $[1, 3]$
2.8.18.60 $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $8$ $1$ $18$ $A_4\times C_2$ (as 8T13) $3$ $1$ $[2, 2, 3]$ $[2, 2, 3]^{3}$ $t + 1$ $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $[11, 6, 4, 0]$ $[1, 3]$
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