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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 $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
5.4.0.1 $x^{4} + 4 x^{2} + 4 x + 2$ $5$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 4 t^{2} + 4 t + 2$ $x - 5$ $[0]$ $[\ ]$
5.4.2.1 $x^{4} + 48 x^{3} + 670 x^{2} + 2256 x + 1449$ $5$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 4 t + 2$ $x^{2} + 20 x + 5$ $[0]$ $[1]$
5.4.2.2 $x^{4} - 20 x^{2} + 50$ $5$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 4 t + 2$ $x^{2} + 5 t$ $[0]$ $[1]$
5.4.3.1 $x^{4} + 20$ $5$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 3$ $x^{4} + 20$ $[0]$ $[1]$
5.4.3.2 $x^{4} + 5$ $5$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 3$ $x^{4} + 5$ $[0]$ $[1]$
5.4.3.3 $x^{4} + 10$ $5$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 3$ $x^{4} + 10$ $[0]$ $[1]$
5.4.3.4 $x^{4} + 15$ $5$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 3$ $x^{4} + 15$ $[0]$ $[1]$
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