| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.19.27 |
$12$ |
$x^{12} + 3 x^{8} + 3 x^{6} + 21$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[2]$ |
$[3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 3 x^{6} + 21$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.38 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{8} + 24$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[2]$ |
$[3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{8} + 24$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.39 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{8} + 6 x^{6} + 15$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[2]$ |
$[3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{8} + 6 x^{6} + 15$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.8 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 12$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[2]$ |
$[3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 12$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.23.109 |
$12$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.155 |
$12$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{2} + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{2} + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.61 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{6} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 18 x^{6} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.64 |
$12$ |
$x^{12} + 9 x^{5} + 9 x^{4} + 9 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 9 x^{5} + 9 x^{4} + 9 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.66 |
$12$ |
$x^{12} + 15 x^{6} + 12 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 15 x^{6} + 12 x^{3} + 9 x + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.72 |
$12$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
