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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
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Results (24 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
3.1.12.21a2.2 $x^{12} + 3 x^{10} + 9 x^{3} + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 3 x^{10} + 9 x^{3} + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.4 $x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.6 $x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.34 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.35 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.36 $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.37 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.38 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.39 $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.40 $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.41 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.42 $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.44 $x^{12} + 6 x^{10} + 9 x^{3} + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 6 x^{10} + 9 x^{3} + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.46 $x^{12} + 6 x^{10} + 9 x^{3} + 9 x^{2} + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 6 x^{10} + 9 x^{3} + 9 x^{2} + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.48 $x^{12} + 6 x^{10} + 9 x^{3} + 18 x^{2} + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $6$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $t + 1$ $x^{12} + 6 x^{10} + 9 x^{3} + 18 x^{2} + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.64 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.65 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.66 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.67 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.68 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.69 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.70 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.71 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
3.1.12.21a2.72 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $21$ $S_3^2:C_6$ (as 12T121) $2$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 6$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ undefined
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