| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.18.80 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$18$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[4/3, 2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.328 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 4 x + 14$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 4 x + 14$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.439 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.15 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.8 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.28.10 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.200 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.202 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.94 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
