| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.1 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 18 x^{4} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.10 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{8} + 51 x^{6} - 36 x^{5} + 36 x^{4} - 18 x^{3} + 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.11 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 792 x^{8} + 1728 x^{7} + 2918 x^{6} + 3684 x^{5} + 3156 x^{4} + 1376 x^{3} - 36 x^{2} - 168 x + 25$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.12 |
$12$ |
$x^{12} + 12 x^{8} - 6 x^{6} + 36 x^{4} - 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6.D_6$ (as 12T39) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.13 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 30 x^{6} - 36 x^{5} + 45 x^{4} - 36 x^{3} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.14 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 45 x^{4} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.15 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 24 x^{6} - 18 x^{5} + 9 x^{4} - 18 x^{3} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.2 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 39 x^{6} + 18 x^{5} + 18 x^{4} + 54 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + \left(3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.3 |
$12$ |
$x^{12} + 30 x^{6} + 72 x^{5} + 36 x^{4} + 36 x^{3} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.4 |
$12$ |
$x^{12} - 6 x^{9} - 12 x^{8} + 24 x^{6} + 72 x^{5} + 72 x^{4} - 18 x^{3} - 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 6 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.5 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.6 |
$12$ |
$x^{12} + 6 x^{8} + 15 x^{6} + 9 x^{4} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.7 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 42 x^{6} - 36 x^{5} + 18 x^{4} + 36 x^{3} - 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + 3 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.8 |
$12$ |
$x^{12} + 42 x^{6} + 72 x^{5} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.9 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{6} + 18 x^{5} + 9 x^{4} + 36 x^{3} + 18 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + \left(3 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
