| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.19.15 |
$12$ |
$x^{12} + 6 x^{9} + 6 x^{8} + 3 x^{6} + 15$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 6 x^{8} + 3 x^{6} + 15$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.33 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 21$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 21$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.5 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.19.7 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{8} + 6 x^{6} + 6$ |
$3$ |
$12$ |
$1$ |
$19$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[2]$ |
$[5/4, 5/4, 3/2, 2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{8} + 6 x^{6} + 6$ |
$[8, 0]$ |
$[2, 2]$ |
| 3.12.21.10 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.13 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.2 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.29 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{6} + 12 x^{3} + 9 x^{2} + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{6} + 12 x^{3} + 9 x^{2} + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.3 |
$12$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 21 x^{3} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 21 x^{3} + 9 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.31 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.37 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{2} + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{2} + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.38 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{2} + 18 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.52 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 18 x + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.63 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 18 x^{2} + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 18 x^{2} + 12$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.65 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 3 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 3 x^{3} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.79 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.23.12 |
$12$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.19 |
$12$ |
$x^{12} + 3 x^{6} + 18 x^{5} + 9 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 18 x^{5} + 9 x^{3} + 9 x + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.23 |
$12$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.25 |
$12$ |
$x^{12} + 3 x^{9} + 18 x^{6} + 18 x^{4} + 12 x^{3} + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 18 x^{6} + 18 x^{4} + 12 x^{3} + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.26 |
$12$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{4} + 6 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{4} + 6 x^{3} + 9 x + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.27 |
$12$ |
$x^{12} + 3 x^{6} + 18 x^{4} + 21 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 18 x^{4} + 21 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.3 |
$12$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 18 x^{3} + 9 x^{2} + 9 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 18 x^{3} + 9 x^{2} + 9 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.31 |
$12$ |
$x^{12} + 15 x^{6} + 9 x^{5} + 18 x^{3} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 15 x^{6} + 9 x^{5} + 18 x^{3} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.34 |
$12$ |
$x^{12} + 3 x^{6} + 9 x^{5} + 9 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 9 x^{5} + 9 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.37 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 21 x^{3} + 18 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 21 x^{3} + 18 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.45 |
$12$ |
$x^{12} + 3 x^{9} + 6 x^{6} + 9 x^{5} + 18 x^{4} + 24 x^{3} + 9 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 6 x^{6} + 9 x^{5} + 18 x^{4} + 24 x^{3} + 9 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.47 |
$12$ |
$x^{12} + 18 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 18 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.5 |
$12$ |
$x^{12} + 3 x^{9} + 24 x^{6} + 9 x^{5} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 24 x^{6} + 9 x^{5} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.54 |
$12$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 18 x^{2} + 9 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 18 x^{2} + 9 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.57 |
$12$ |
$x^{12} + 3 x^{6} + 18 x^{4} + 12 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 18 x^{4} + 12 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.58 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 9 x^{4} + 9 x^{2} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 9 x^{4} + 9 x^{2} + 18 x + 15$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.62 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{4} + 18 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{4} + 18 x^{2} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.70 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.8 |
$12$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 9 x^{4} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 9 x^{4} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.83 |
$12$ |
$x^{12} + 3 x^{9} + 24 x^{6} + 9 x^{5} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 24 x^{6} + 9 x^{5} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.87 |
$12$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 18 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 18 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.9 |
$12$ |
$x^{12} + 18 x^{6} + 9 x^{5} + 9 x^{4} + 9 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 18 x^{6} + 9 x^{5} + 9 x^{4} + 9 x^{2} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.95 |
$12$ |
$x^{12} + 3 x^{6} + 18 x^{5} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 18 x^{5} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.99 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
