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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
13.4.0.1 $x^{4} + 3 x^{2} + 12 x + 2$ $13$ $1$ $4$ $0$ $C_4$ (as 4T1) $4$ $1$ $[\ ]$ $[\ ]^{4}$ $t^{4} + 3 t^{2} + 12 t + 2$ $x - 13$ $[0]$ $[\ ]$
13.4.2.1 $x^{4} + 284 x^{3} + 21754 x^{2} + 225780 x + 59193$ $13$ $2$ $2$ $2$ $C_2^2$ (as 4T2) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 12 t + 2$ $x^{2} + 130 x + 13$ $[0]$ $[1]$
13.4.2.2 $x^{4} - 156 x^{2} + 338$ $13$ $2$ $2$ $2$ $C_4$ (as 4T1) $2$ $2$ $[\ ]$ $[\ ]_{2}^{2}$ $t^{2} + 12 t + 2$ $x^{2} + 13 t$ $[0]$ $[1]$
13.4.3.1 $x^{4} + 52$ $13$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 11$ $x^{4} + 52$ $[0]$ $[1]$
13.4.3.2 $x^{4} + 13$ $13$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 11$ $x^{4} + 13$ $[0]$ $[1]$
13.4.3.3 $x^{4} + 26$ $13$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 11$ $x^{4} + 26$ $[0]$ $[1]$
13.4.3.4 $x^{4} + 91$ $13$ $4$ $1$ $3$ $C_4$ (as 4T1) $1$ $4$ $[\ ]$ $[\ ]_{4}$ $t + 11$ $x^{4} + 91$ $[0]$ $[1]$
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