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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 (5 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
11.4.0.1 $x^{4} + 8 x^{2} + 10 x + 2$ $11$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 8 t^{2} + 10 t + 2$ $x - 11$ $[0]$ $[\ ]$
11.4.2.1 $x^{4} + 14 x^{3} + 75 x^{2} + 182 x + 620$ $11$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 7 t + 2$ $x^{2} + 11$ $[0]$ $[1]$
11.4.2.2 $x^{4} - 77 x^{2} + 242$ $11$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 7 t + 2$ $x^{2} + 11 t$ $[0]$ $[1]$
11.4.3.1 $x^{4} + 11$ $11$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 9$ $x^{4} + 11$ $[0]$ $[2]$
11.4.3.2 $x^{4} + 22$ $11$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 9$ $x^{4} + 22$ $[0]$ $[2]$
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