| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.4 |
$12$ |
$x^{12} - 6 x^{9} - 12 x^{8} + 24 x^{6} + 72 x^{5} + 72 x^{4} - 18 x^{3} - 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 6 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.7 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 42 x^{6} - 36 x^{5} + 18 x^{4} + 36 x^{3} - 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + 3 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.18.19 |
$12$ |
$x^{12} - 6 x^{11} + 33 x^{10} + 108 x^{9} + 108 x^{8} + 36 x^{7} + 51 x^{6} - 126 x^{5} - 252 x^{4} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 t x^{4} + \left(3 t + 3\right) x^{3} + 21$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.64 |
$12$ |
$x^{12} - 6 x^{10} + 18 x^{8} + 6 x^{6} - 18 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{4} + 3$ |
$[4, 0]$ |
$[2, 1]$ |
