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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (20 matches)

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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
7.12.1.0a1.1 $x^{12} + 2 x^{8} + 5 x^{7} + 3 x^{6} + 2 x^{5} + 4 x^{4} + 5 x^{2} + 3$ $7$ $12$ $1$ $0$ $C_{12}$ (as 12T1) $12$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{12}$ $[\ ]^{12}$ $[\ ]$ $[\ ]$ $t^{12} + 2 t^{8} + 5 t^{7} + 3 t^{6} + 2 t^{5} + 4 t^{4} + 5 t^{2} + 3$ $x - 7$ $[0]$ $[\ ]$ undefined
7.6.2.6a1.1 $( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{2} + 7 x$ $7$ $6$ $2$ $6$ $C_{12}$ (as 12T1) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ $x^{2} + 7 t$ $[0]$ $[1]$ $z + 2$ undefined
7.6.2.6a1.2 $( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{2} + 7$ $7$ $6$ $2$ $6$ $C_6\times C_2$ (as 12T2) $6$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{6}$ $[\ ]_{2}^{6}$ $[\ ]$ $[\ ]$ $t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ $x^{2} + 7$ $[0]$ $[1]$ $z + 2$ undefined
7.4.3.8a1.1 $( x^{4} + 5 x^{2} + 4 x + 3 )^{3} + 7 x^{2}$ $7$ $4$ $3$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{4}$ $[\ ]_{3}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 5 t^{2} + 4 t + 3$ $x^{3} + 7 t^{2}$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
7.4.3.8a1.2 $( x^{4} + 5 x^{2} + 4 x + 3 )^{3} + 7 x$ $7$ $4$ $3$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{4}$ $[\ ]_{3}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 5 t^{2} + 4 t + 3$ $x^{3} + 7 t$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
7.4.3.8a1.3 $( x^{4} + 5 x^{2} + 4 x + 3 )^{3} + 7$ $7$ $4$ $3$ $8$ $C_{12}$ (as 12T1) $4$ $3$ $[\ ]$ $[\ ]$ $[\ ]_{3}^{4}$ $[\ ]_{3}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 5 t^{2} + 4 t + 3$ $x^{3} + 7$ $[0]$ $[1]$ $z^2 + 3 z + 3$ undefined
7.3.4.9a1.1 $( x^{3} + 6 x^{2} + 4 )^{4} + 7 x$ $7$ $3$ $4$ $9$ $D_4 \times C_3$ (as 12T14) $6$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{6}$ $[\ ]_{4}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $t^{3} + 6 t^{2} + 4$ $x^{4} + 7 t$ $[0]$ $[2]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
7.3.4.9a1.2 $( x^{3} + 6 x^{2} + 4 )^{4} + 7$ $7$ $3$ $4$ $9$ $D_4 \times C_3$ (as 12T14) $6$ $4$ $[\ ]$ $[\ ]$ $[\ ]_{4}^{6}$ $[\ ]_{4}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $t^{3} + 6 t^{2} + 4$ $x^{4} + 7$ $[0]$ $[2]$ $z^3 + 4 z^2 + 6 z + 4$ undefined
7.2.6.10a1.1 $( x^{2} + 6 x + 3 )^{6} + 7 x$ $7$ $2$ $6$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7 t$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.2.6.10a1.2 $( x^{2} + 6 x + 3 )^{6} + 7$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ $[1]$
7.2.6.10a1.3 $( x^{2} + 6 x + 3 )^{6} + 7 x + 7$ $7$ $2$ $6$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7 t + 7$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.2.6.10a1.4 $( x^{2} + 6 x + 3 )^{6} + 7 x + 28$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 7 t + 28$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.2.6.10a1.5 $( x^{2} + 6 x + 3 )^{6} + 35 x + 28$ $7$ $2$ $6$ $10$ $C_{12}$ (as 12T1) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 35 t + 28$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.2.6.10a1.6 $( x^{2} + 6 x + 3 )^{6} + 14 x + 42$ $7$ $2$ $6$ $10$ $C_6\times C_2$ (as 12T2) $2$ $6$ $[\ ]$ $[\ ]$ $[\ ]_{6}^{2}$ $[\ ]_{6}^{2}$ $[\ ]$ $[\ ]$ $t^{2} + 6 t + 3$ $x^{6} + 14 t + 42$ $[0]$ $[1]$ $z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.1.12.11a1.1 $x^{12} + 7$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 7$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ $[2]$
7.1.12.11a1.2 $x^{12} + 14$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 14$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
7.1.12.11a1.3 $x^{12} + 21$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 21$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
7.1.12.11a1.4 $x^{12} + 28$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 28$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
7.1.12.11a1.5 $x^{12} + 35$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 35$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
7.1.12.11a1.6 $x^{12} + 42$ $7$ $1$ $12$ $11$ $D_4 \times C_3$ (as 12T14) $2$ $12$ $[\ ]$ $[\ ]$ $[\ ]_{12}^{2}$ $[\ ]_{12}^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $t + 4$ $x^{12} + 42$ $[0]$ $[2]$ $z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
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