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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
5.6.0.1 $x^{6} + x^{4} + 4 x^{3} + x^{2} + 2$ $5$ $1$ $6$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]^{6}$ $t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ $x - 5$ $[0]$ $[\ ]$
5.6.3.1 $x^{6} + 60 x^{5} + 1221 x^{4} + 8846 x^{3} + 9864 x^{2} + 29208 x + 29309$ $5$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 3 t + 3$ $x^{2} + 20 x + 5$ $[0]$ $[1]$
5.6.3.2 $x^{6} + 75 x^{2} - 375$ $5$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 3 t + 3$ $x^{2} + 5 t$ $[0]$ $[1]$
5.6.4.1 $x^{6} + 12 x^{5} + 54 x^{4} + 122 x^{3} + 168 x^{2} + 228 x + 233$ $5$ $3$ $2$ $4$ $S_3$ (as 6T2) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 4 t + 2$ $x^{3} + 5$ $[0]$ $[1]$
5.6.4.2 $x^{6} + 10 x^{3} - 25$ $5$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $6$ $3$ $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 4 t + 2$ $x^{3} + 5 t + 15$ $[0]$ $[1]$
5.6.5.1 $x^{6} + 5$ $5$ $6$ $1$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t + 3$ $x^{6} + 5$ $[0]$ $[2]$
5.6.5.2 $x^{6} + 10$ $5$ $6$ $1$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t + 3$ $x^{6} + 10$ $[0]$ $[2]$
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