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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
17.6.0.1 $x^{6} + 2 x^{4} + 10 x^{2} + 3 x + 3$ $17$ $1$ $6$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]^{6}$ $t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ $x - 17$ $[0]$ $[\ ]$
17.6.3.1 $x^{6} + 459 x^{5} + 70280 x^{4} + 3597823 x^{3} + 1271380 x^{2} + 4696159 x + 50437479$ $17$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + t + 14$ $x^{2} + 153 x + 17$ $[0]$ $[1]$
17.6.3.2 $x^{6} + 289 x^{2} - 68782$ $17$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + t + 14$ $x^{2} + 17 t$ $[0]$ $[1]$
17.6.4.1 $x^{6} + 48 x^{5} + 879 x^{4} + 7682 x^{3} + 44916 x^{2} + 265428 x + 127425$ $17$ $3$ $2$ $4$ $S_3$ (as 6T2) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 16 t + 3$ $x^{3} + 51 x + 17$ $[0]$ $[1]$
17.6.4.2 $x^{6} + 204 x^{3} - 7225$ $17$ $3$ $2$ $4$ $S_3\times C_3$ (as 6T5) $6$ $3$ $[\ ]$ $[\ ]_{3}^{6}$ $t^{2} + 16 t + 3$ $x^{3} + 17 t + 238$ $[0]$ $[1]$
17.6.5.1 $x^{6} + 17$ $17$ $6$ $1$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t + 14$ $x^{6} + 17$ $[0]$ $[2]$
17.6.5.2 $x^{6} + 51$ $17$ $6$ $1$ $5$ $D_{6}$ (as 6T3) $2$ $6$ $[\ ]$ $[\ ]_{6}^{2}$ $t + 14$ $x^{6} + 51$ $[0]$ $[2]$
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