| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.29 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{7} - 2 x^{6} + 4 x^{4} + 8 x^{3} - 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + 2 x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.16.12 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 2 x^{9} + 8 x^{8} - 4 x^{7} + 10 x^{6} + 4 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 2\right) x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.20.1 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 24 x^{7} + 18 x^{6} + 4 x^{5} - 8 x^{4} - 24 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.13 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 12 x^{8} + 12 x^{7} + 26 x^{6} + 36 x^{5} + 48 x^{4} + 64 x^{3} + 52 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 2\right) x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.23 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 32 x^{8} + 8 x^{7} + 10 x^{6} - 12 x^{5} + 16 x^{4} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.26 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 4 x^{9} + 18 x^{6} - 20 x^{5} - 8 x^{4} + 48 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 t x^{3} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.44 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 52 x^{8} - 24 x^{7} + 18 x^{6} + 16 x^{5} + 12 x^{4} + 32 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.45 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 24 x^{9} + 36 x^{8} + 4 x^{7} + 10 x^{6} + 28 x^{5} + 24 x^{4} + 24 x^{3} + 52 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 6 x^{4} + \left(4 t + 2\right) x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.5 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 12 x^{9} + 32 x^{8} + 16 x^{7} - 22 x^{6} + 16 x^{5} + 28 x^{4} + 32 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.8 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 24 x^{8} + 32 x^{7} + 10 x^{6} - 4 x^{5} + 40 x^{4} + 24 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.22.16 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 48 x^{9} + 40 x^{8} + 12 x^{7} + 2 x^{6} - 48 x^{5} - 32 x^{4} - 8 x^{3} + 4 x^{2} + 96 x + 156$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 4 t x + 14 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.17 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 12 x^{9} + 40 x^{8} - 12 x^{7} + 34 x^{6} + 48 x^{5} + 8 x^{4} + 56 x^{3} + 4 x^{2} + 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 4 t x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 6 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.21 |
$12$ |
$x^{12} + 4 x^{10} - 4 x^{9} + 16 x^{8} + 38 x^{6} - 8 x^{5} + 16 x^{4} + 64 x^{3} + 4 x^{2} - 8 x + 4$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 2 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.46 |
$12$ |
$x^{12} + 8 x^{11} + 16 x^{10} + 8 x^{9} + 38 x^{8} + 24 x^{7} + 30 x^{6} + 80 x^{5} + 12 x^{4} + 56 x^{3} + 72 x^{2} + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 4 x^{3} + \left(2 t + 4\right) x^{2} + 10 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.51 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 8 x^{8} + 12 x^{7} + 34 x^{6} + 72 x^{5} + 8 x^{4} - 16 x^{3} + 4 x^{2} + 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 4/3, 4/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 6 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.52 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 32 x^{9} + 28 x^{8} + 24 x^{7} + 38 x^{6} + 56 x^{5} + 72 x^{4} - 8 x^{3} + 60 x^{2} + 76$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 10 t + 4$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.59 |
$12$ |
$x^{12} + 4 x^{11} + 20 x^{10} + 4 x^{9} + 32 x^{8} + 24 x^{7} + 54 x^{6} + 16 x^{4} + 64 x^{3} + 4 x^{2} - 8 x + 4$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 2 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.66 |
$12$ |
$x^{12} + 12 x^{10} + 40 x^{8} - 4 x^{7} + 34 x^{6} - 24 x^{5} + 64 x^{4} - 8 x^{3} + 36 x^{2} + 64 x + 172$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 2 x^{2} + 4 t x + 14 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.68 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} + 12 x^{9} + 48 x^{7} + 78 x^{6} + 16 x^{5} + 32 x^{4} + 96 x^{3} + 52 x^{2} + 24 x + 84$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 2 x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 10 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.9 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 12 x^{9} + 48 x^{8} - 24 x^{7} + 30 x^{6} + 40 x^{5} + 32 x^{4} + 96 x^{3} + 52 x^{2} + 24 x + 84$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 10 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
