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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
7.4.0.1 $x^{4} + 5 x^{2} + 4 x + 3$ $7$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 5 t^{2} + 4 t + 3$ $x - 7$ $[0]$ $[\ ]$
7.4.2.1 $x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 268$ $7$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 6 t + 3$ $x^{2} + 7$ $[0]$ $[1]$
7.4.2.2 $x^{4} - 42 x^{2} + 147$ $7$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 6 t + 3$ $x^{2} + 7 t$ $[0]$ $[1]$
7.4.3.1 $x^{4} + 7$ $7$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 4$ $x^{4} + 7$ $[0]$ $[2]$
7.4.3.2 $x^{4} + 21$ $7$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 4$ $x^{4} + 21$ $[0]$ $[2]$
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