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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 Visible slopes Slope content Unram. Ext. Eisen. Poly.
7.9.0.1 $x^{9} + 6 x^{4} + x^{3} + 6 x + 4$ $7$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 6 t^{4} + t^{3} + 6 t + 4$ $x - 7$
7.9.6.1 $x^{9} + 18 x^{8} + 108 x^{7} + 249 x^{6} + 396 x^{5} + 1944 x^{4} + 2631 x^{3} - 2358 x^{2} - 756 x + 11915$ $7$ $3$ $3$ $6$ $C_3^2$ (as 9T2) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{3} + 7$
7.9.6.2 $x^{9} + 252 x^{6} - 2352 x^{3} + 5488$ $7$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{3} + 7 t^{2}$
7.9.6.3 $x^{9} - 42 x^{6} - 1372$ $7$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{3} + 7 t$
7.9.8.1 $x^{9} + 14$ $7$ $9$ $1$ $8$ $C_9:C_3$ (as 9T6) $[\ ]$ $[\ ]_{9}^{3}$ $t + 4$ $x^{9} + 14$
7.9.8.2 $x^{9} + 7$ $7$ $9$ $1$ $8$ $C_9:C_3$ (as 9T6) $[\ ]$ $[\ ]_{9}^{3}$ $t + 4$ $x^{9} + 7$
7.9.8.3 $x^{9} + 21$ $7$ $9$ $1$ $8$ $C_9:C_3$ (as 9T6) $[\ ]$ $[\ ]_{9}^{3}$ $t + 4$ $x^{9} + 21$
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