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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
13.6.0.1 $x^{6} + 10 x^{3} + 11 x^{2} + 11 x + 2$ $13$ $1$ $6$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]^{6}$ $t^{6} + 10 t^{3} + 11 t^{2} + 11 t + 2$ $x - 13$ $[0]$ $[\ ]$
13.6.3.1 $x^{6} + 390 x^{5} + 50743 x^{4} + 2208202 x^{3} + 765301 x^{2} + 5017316 x + 24555184$ $13$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 2 t + 11$ $x^{2} + 130 x + 13$ $[0]$ $[1]$
13.6.3.2 $x^{6} + 338 x^{2} - 24167$ $13$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 2 t + 11$ $x^{2} + 13 t$ $[0]$ $[1]$
13.6.4.1 $x^{6} + 130 x^{3} - 1521$ $13$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 12 t + 2$ $x^{3} + 13 t + 143$ $[0]$ $[1]$
13.6.4.2 $x^{6} - 156 x^{3} + 338$ $13$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 12 t + 2$ $x^{3} + 13 t$ $[0]$ $[1]$
13.6.4.3 $x^{6} + 36 x^{5} + 438 x^{4} + 1898 x^{3} + 1344 x^{2} + 5604 x + 21705$ $13$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 12 t + 2$ $x^{3} + 13$ $[0]$ $[1]$
13.6.5.1 $x^{6} + 52$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 52$ $[0]$ $[1]$
13.6.5.2 $x^{6} + 13$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 13$ $[0]$ $[1]$
13.6.5.3 $x^{6} + 39$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 39$ $[0]$ $[1]$
13.6.5.4 $x^{6} + 26$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 26$ $[0]$ $[1]$
13.6.5.5 $x^{6} + 65$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 65$ $[0]$ $[1]$
13.6.5.6 $x^{6} + 78$ $13$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 11$ $x^{6} + 78$ $[0]$ $[1]$
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