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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 (12 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
19.6.0.1 $x^{6} + 17 x^{3} + 17 x^{2} + 6 x + 2$ $19$ $1$ $6$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]^{6}$ $t^{6} + 17 t^{3} + 17 t^{2} + 6 t + 2$ $x - 19$ $[0]$ $[\ ]$
19.6.3.1 $x^{6} + 1444 x^{2} - 116603$ $19$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 4 t + 17$ $x^{2} + 19 t$ $[0]$ $[1]$
19.6.3.2 $x^{6} + 65 x^{4} + 34 x^{3} + 1099 x^{2} - 1802 x + 4564$ $19$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 4 t + 17$ $x^{2} + 19$ $[0]$ $[1]$
19.6.4.1 $x^{6} + 304 x^{3} - 5415$ $19$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 18 t + 2$ $x^{3} + 19 t + 323$ $[0]$ $[1]$
19.6.4.2 $x^{6} - 342 x^{3} + 722$ $19$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 18 t + 2$ $x^{3} + 19 t$ $[0]$ $[1]$
19.6.4.3 $x^{6} + 54 x^{5} + 1168 x^{4} + 12926 x^{3} + 104347 x^{2} + 738556 x + 220465$ $19$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 18 t + 2$ $x^{3} + 95 x + 19$ $[0]$ $[1]$
19.6.5.1 $x^{6} + 38$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 38$ $[0]$ $[1]$
19.6.5.2 $x^{6} + 152$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 152$ $[0]$ $[1]$
19.6.5.3 $x^{6} + 190$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 190$ $[0]$ $[1]$
19.6.5.4 $x^{6} + 76$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 76$ $[0]$ $[1]$
19.6.5.5 $x^{6} + 19$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 19$ $[0]$ $[1]$
19.6.5.6 $x^{6} + 95$ $19$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 17$ $x^{6} + 95$ $[0]$ $[1]$
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