| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.16.1 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 4 x^{9} - 4 x^{7} + 10 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.14 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} - 2 x^{9} + 12 x^{8} - 4 x^{7} + 10 x^{6} - 4 x^{5} + 4 x^{4} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.17 |
$12$ |
$x^{12} - 2 x^{10} - 2 x^{9} + 8 x^{8} + 8 x^{7} - 2 x^{6} - 4 x^{5} + 12 x^{4} + 8 x^{3} - 4 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{4} + 2 t x^{3} + 2 x^{2} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.4 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 14 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{3} + 4 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.20.10 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 52 x^{8} - 12 x^{7} + 18 x^{6} + 40 x^{5} + 24 x^{4} + 32 x^{3} + 36 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + \left(4 t + 2\right) x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.11 |
$12$ |
$x^{12} + 2 x^{11} - 2 x^{10} + 12 x^{9} + 40 x^{8} + 4 x^{7} - 18 x^{6} + 12 x^{5} + 76 x^{4} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 6 t x^{4} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.17 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} - 4 x^{9} + 16 x^{8} - 12 x^{7} + 26 x^{6} + 16 x^{5} + 40 x^{4} + 12 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{4} + 6 x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.18 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 12 x^{9} + 24 x^{8} + 12 x^{7} + 26 x^{6} + 4 x^{5} + 80 x^{4} + 24 x^{3} + 20 x^{2} + 32 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 t x^{3} + 2 x^{2} + 4 t x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.19 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 12 x^{9} + 28 x^{8} + 36 x^{7} + 74 x^{6} + 48 x^{5} + 72 x^{4} + 8 x^{3} + 44 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.22 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 4 x^{9} + 22 x^{8} + 20 x^{7} + 34 x^{6} + 8 x^{5} + 72 x^{4} + 48 x^{3} + 16 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + 6 t x^{2} + 4 t x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.24 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 64 x^{8} - 36 x^{7} + 90 x^{6} - 8 x^{5} + 48 x^{4} + 32 x^{3} + 12 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.32 |
$12$ |
$x^{12} + 2 x^{11} + 10 x^{10} + 20 x^{9} + 32 x^{8} + 36 x^{7} + 46 x^{6} + 60 x^{5} + 36 x^{4} - 24 x^{3} - 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + 6 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.36 |
$12$ |
$x^{12} + 2 x^{11} + 10 x^{10} + 8 x^{9} + 32 x^{8} + 12 x^{7} + 46 x^{6} - 12 x^{5} + 36 x^{4} + 48 x^{3} - 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 4\right) x^{4} + 4 t x^{3} + 6 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.42 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 46 x^{6} + 12 x^{5} + 24 x^{4} + 28 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + \left(4 t + 2\right) x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.43 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} + 8 x^{9} + 20 x^{8} + 4 x^{7} + 42 x^{6} + 40 x^{5} + 40 x^{4} + 16 x^{3} + 40 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x^{4} + \left(4 t + 4\right) x^{2} + 4 t x + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.46 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 16 x^{9} + 44 x^{8} + 52 x^{7} + 54 x^{6} + 20 x^{5} + 76 x^{4} + 48 x^{3} + 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(6 t + 4\right) x^{4} + 4 t x^{3} + \left(4 t + 6\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.47 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 20 x^{8} + 24 x^{7} + 46 x^{6} + 12 x^{5} + 40 x^{4} + 32 x^{3} + 52 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + \left(4 t + 6\right) x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.49 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 32 x^{8} + 16 x^{7} + 38 x^{6} + 44 x^{5} + 40 x^{4} + 16 x^{3} + 28 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 2 x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.51 |
$12$ |
$x^{12} + 2 x^{11} - 2 x^{10} + 16 x^{9} + 52 x^{8} + 36 x^{7} + 46 x^{6} + 36 x^{5} + 84 x^{4} + 24 x^{3} + 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 6 t x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 2\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.9 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 32 x^{9} + 64 x^{8} + 80 x^{7} + 102 x^{6} + 92 x^{5} + 56 x^{4} + 40 x^{3} + 4 x^{2} - 8 x + 4$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.22.10 |
$12$ |
$x^{12} + 4 x^{10} + 6 x^{8} + 8 x^{7} + 22 x^{6} + 16 x^{5} + 64 x^{4} + 8 x^{3} + 88 x^{2} + 72 x + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + \left(6 t + 4\right) x^{2} + 4 x + 6 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.13 |
$12$ |
$x^{12} + 4 x^{11} + 28 x^{10} + 20 x^{9} + 64 x^{8} - 4 x^{7} + 122 x^{6} + 24 x^{5} + 176 x^{4} - 24 x^{3} + 124 x^{2} + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 4 t x + 6 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.14 |
$12$ |
$x^{12} + 8 x^{10} + 40 x^{8} + 62 x^{6} + 152 x^{4} + 84 x^{2} + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 6 x^{2} + 10 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.15 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} + 20 x^{9} + 24 x^{8} + 32 x^{7} + 70 x^{6} + 80 x^{5} + 48 x^{4} + 56 x^{3} + 44 x^{2} + 56 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 4 x + 2 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.19 |
$12$ |
$x^{12} + 4 x^{11} + 20 x^{10} + 12 x^{9} + 40 x^{8} + 24 x^{7} + 30 x^{6} + 64 x^{5} + 56 x^{3} - 4 x^{2} - 40 x + 100$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 4 x + 10 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.2 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 48 x^{9} + 32 x^{8} - 8 x^{7} + 14 x^{6} + 72 x^{5} + 52 x^{4} - 16 x^{3} + 16 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{2} + 4 x + 2 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.20 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 24 x^{9} + 40 x^{8} - 4 x^{7} + 34 x^{6} + 72 x^{5} - 32 x^{4} + 8 x^{3} + 4 x^{2} + 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 6 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.22 |
$12$ |
$x^{12} + 12 x^{10} - 4 x^{9} + 48 x^{8} - 28 x^{7} + 106 x^{6} - 48 x^{5} + 176 x^{4} - 24 x^{3} + 124 x^{2} + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 4 t x + 6 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.23 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 4 x^{9} + 24 x^{8} + 8 x^{7} + 22 x^{6} + 8 x^{5} + 48 x^{4} + 56 x^{3} + 44 x^{2} + 56 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 4 x + 2 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.28 |
$12$ |
$x^{12} + 8 x^{11} + 16 x^{10} + 8 x^{9} + 44 x^{8} - 4 x^{7} + 6 x^{6} + 48 x^{5} - 4 x^{4} + 24 x^{3} + 16 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + 4 t x + 2 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.35 |
$12$ |
$x^{12} + 4 x^{11} + 20 x^{10} + 8 x^{9} + 24 x^{7} + 22 x^{6} + 104 x^{5} + 44 x^{4} - 16 x^{3} + 48 x^{2} + 56 x + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{2} + 4 x + 10 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.36 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 20 x^{9} + 56 x^{8} + 20 x^{7} + 50 x^{6} + 80 x^{5} + 32 x^{3} + 4 x^{2} + 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 6 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.5 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 20 x^{9} + 56 x^{8} + 20 x^{7} + 66 x^{6} + 48 x^{5} + 96 x^{4} + 64 x^{3} + 36 x^{2} + 56 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 6 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.50 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 24 x^{9} + 40 x^{8} - 4 x^{7} + 50 x^{6} + 40 x^{5} + 64 x^{4} + 8 x^{3} + 36 x^{2} + 56 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 6 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.56 |
$12$ |
$x^{12} + 12 x^{10} + 8 x^{9} + 36 x^{8} + 44 x^{7} + 38 x^{6} - 24 x^{5} + 116 x^{4} + 88 x^{3} + 16 x^{2} - 32 x + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 4 x^{3} + 4 t x + 2 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.57 |
$12$ |
$x^{12} - 4 x^{11} + 24 x^{10} + 8 x^{9} + 40 x^{8} - 24 x^{7} + 54 x^{6} + 72 x^{4} + 36 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + \left(4 t + 6\right) x^{4} + 6 x^{2} + 2 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.58 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 16 x^{7} + 14 x^{6} + 24 x^{5} + 56 x^{3} - 4 x^{2} - 40 x + 100$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 4 x + 10 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.62 |
$12$ |
$x^{12} - 4 x^{11} + 24 x^{10} + 8 x^{9} + 28 x^{8} + 32 x^{7} - 2 x^{6} + 112 x^{5} + 32 x^{4} + 76 x^{2} - 40 x + 100$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 2\right) x^{2} + 4 x + 10 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.65 |
$12$ |
$x^{12} - 4 x^{11} + 16 x^{10} + 4 x^{9} + 10 x^{8} + 48 x^{7} + 14 x^{6} + 88 x^{5} + 36 x^{4} + 56 x^{3} + 96 x^{2} + 76$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + \left(4 t + 4\right) x^{3} + 6 t x^{2} + 10 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.67 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 32 x^{8} + 20 x^{7} + 74 x^{6} - 40 x^{5} + 80 x^{4} + 8 x^{3} + 28 x^{2} + 32 x + 28$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 4 t x + 6 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
