Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.19.11 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 3$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 3$ |
$[8, 0]$ |
$[2, 2]$ |
3.12.19.6 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{6} + 24$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{6} + 24$ |
$[8, 0]$ |
$[2, 2]$ |
3.12.21.14 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x + 12$ |
$[10, 0]$ |
$[2, 2]$ |
3.12.21.30 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x + 15$ |
$[10, 0]$ |
$[2, 2]$ |
3.12.21.36 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 24$ |
$[10, 0]$ |
$[2, 2]$ |
3.12.21.49 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 21 x^{3} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 21 x^{3} + 9 x + 12$ |
$[10, 0]$ |
$[2, 2]$ |
3.12.21.8 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 15 x^{3} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 15 x^{3} + 24$ |
$[10, 0]$ |
$[2, 2]$ |
3.12.21.9 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 12$ |
$[10, 0]$ |
$[2, 2]$ |