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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
7.6.0.1 $x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3$ $7$ $1$ $6$ $0$ $C_6$ (as 6T1) $6$ $1$ $[\ ]$ $[\ ]^{6}$ $t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ $x - 7$ $[0]$ $[\ ]$
7.6.3.1 $x^{6} + 861 x^{5} + 33033 x^{4} + 1385475 x^{3} + 277830 x^{2} + 8232 x - 1372$ $7$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{2} + \left(28 t^{2} + 42 t + 35\right) x + 7 t$ $[0]$ $[1]$
7.6.3.2 $x^{6} + 12 x^{5} + 57 x^{4} + 176 x^{3} + 699 x^{2} + 420 x + 1787$ $7$ $2$ $3$ $3$ $C_6$ (as 6T1) $3$ $2$ $[\ ]$ $[\ ]_{2}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{2} + 7$ $[0]$ $[1]$
7.6.4.1 $x^{6} + 14 x^{3} - 245$ $7$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{3} + 7 t + 28$ $[0]$ $[1]$
7.6.4.2 $x^{6} - 42 x^{3} + 147$ $7$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{3} + 7 t$ $[0]$ $[1]$
7.6.4.3 $x^{6} + 18 x^{5} + 117 x^{4} + 338 x^{3} + 477 x^{2} + 792 x + 1210$ $7$ $3$ $2$ $4$ $C_6$ (as 6T1) $2$ $3$ $[\ ]$ $[\ ]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{3} + 7$ $[0]$ $[1]$
7.6.5.1 $x^{6} + 21$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 21$ $[0]$ $[1]$
7.6.5.2 $x^{6} + 42$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 42$ $[0]$ $[1]$
7.6.5.3 $x^{6} + 35$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 35$ $[0]$ $[1]$
7.6.5.4 $x^{6} + 14$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 14$ $[0]$ $[1]$
7.6.5.5 $x^{6} + 7$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 7$ $[0]$ $[1]$
7.6.5.6 $x^{6} + 28$ $7$ $6$ $1$ $5$ $C_6$ (as 6T1) $1$ $6$ $[\ ]$ $[\ ]_{6}$ $t + 4$ $x^{6} + 28$ $[0]$ $[1]$
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