Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.9.1 |
$12$ |
$x^{12} + 18 x^{4} - 27$ |
$3$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3 t$ |
$[0]$ |
$[2]$ |
3.12.9.2 |
$12$ |
$x^{12} + 8 x^{10} + 4 x^{9} + 33 x^{8} + 24 x^{7} - 10 x^{6} - 96 x^{5} + 163 x^{4} + 12 x^{3} - 6 x^{2} + 68 x + 172$ |
$3$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3$ |
$[0]$ |
$[2]$ |
3.12.19.19 |
$12$ |
$x^{12} + 6 x^{8} + 21$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 21$ |
$[8, 0]$ |
$[1, 2]$ |
3.12.19.24 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 24$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 24$ |
$[8, 0]$ |
$[1, 2]$ |
3.12.19.30 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 6 x^{6} + 6$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 6 x^{6} + 6$ |
$[8, 0]$ |
$[1, 2]$ |
3.12.19.40 |
$12$ |
$x^{12} + 6 x^{8} + 12$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 12$ |
$[8, 0]$ |
$[1, 2]$ |
3.12.19.43 |
$12$ |
$x^{12} + 6 x^{8} + 3$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[1, 2]$ |
3.12.19.47 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 15$ |
$3$ |
$12$ |
$1$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 15$ |
$[8, 0]$ |
$[1, 2]$ |