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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
3.4.0.1 $x^{4} + 2 x^{3} + 2$ $3$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 2 t^{3} + 2$ $x - 3$ $[0]$ $[\ ]$
3.4.2.1 $x^{4} + 4 x^{3} + 14 x^{2} + 20 x + 13$ $3$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{2} + 3$ $[0]$ $[1]$
3.4.2.2 $x^{4} - 6 x^{3} + 12 x^{2} + 36 x + 18$ $3$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{2} + 3 t x + 3 t$ $[0]$ $[1]$
3.4.3.1 $x^{4} + 3$ $3$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 1$ $x^{4} + 3$ $[0]$ $[2]$
3.4.3.2 $x^{4} + 6$ $3$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 1$ $x^{4} + 6$ $[0]$ $[2]$
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