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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
23.4.0.1 $x^{4} + 3 x^{2} + 19 x + 5$ $23$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 3 t^{2} + 19 t + 5$ $x - 23$ $[0]$ $[\ ]$
23.4.2.1 $x^{4} + 42 x^{3} + 497 x^{2} + 1176 x + 10467$ $23$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 21 t + 5$ $x^{2} + 23$ $[0]$ $[1]$
23.4.2.2 $x^{4} - 483 x^{2} + 2645$ $23$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 21 t + 5$ $x^{2} + 23 t$ $[0]$ $[1]$
23.4.3.1 $x^{4} + 23$ $23$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 18$ $x^{4} + 23$ $[0]$ $[2]$
23.4.3.2 $x^{4} + 115$ $23$ $4$ $1$ $3$ $D_{4}$ (as 4T3) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t + 18$ $x^{4} + 115$ $[0]$ $[2]$
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