| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.27 |
$12$ |
$x^{12} + 4 x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{4} - 4 x^{3} + 12 x^{2} - 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + 2 t x + 2$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.16.16 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 16 x^{8} + 16 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.20.2 |
$12$ |
$x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 30 x^{8} + 24 x^{7} + 76 x^{6} + 72 x^{5} + 120 x^{4} + 40 x^{3} + 60 x^{2} + 8 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(6 t + 6\right) x^{4} + 4 t x^{3} + \left(6 t + 4\right) x^{2} + 4 t x + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.20 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 24 x^{9} + 48 x^{8} + 40 x^{7} + 36 x^{6} + 24 x^{5} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.35 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 40 x^{8} + 32 x^{7} + 44 x^{6} + 72 x^{5} + 68 x^{4} + 96 x^{3} + 88 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.40 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 24 x^{8} + 32 x^{7} + 28 x^{6} + 24 x^{5} + 36 x^{4} + 48 x^{3} + 88 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + 6 x^{2} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.22.32 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 28 x^{9} + 72 x^{8} - 36 x^{7} + 96 x^{6} - 56 x^{5} + 180 x^{4} - 32 x^{3} + 64 x^{2} - 24 x + 156$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 t x + 4 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.34 |
$12$ |
$x^{12} + 12 x^{10} + 48 x^{8} + 76 x^{6} + 60 x^{4} + 24 x^{2} + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 6 x^{2} + 8 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.41 |
$12$ |
$x^{12} + 4 x^{10} + 8 x^{8} + 8 x^{7} + 4 x^{6} + 16 x^{5} - 4 x^{4} + 16 x^{3} + 8 x^{2} - 16 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{2} + 4 x + 8 t + 2$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.55 |
$12$ |
$x^{12} - 4 x^{7} - 4 x^{6} + 16 x^{2} + 56 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x + 8 t + 2$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.64 |
$12$ |
$x^{12} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 16 x^{7} + 44 x^{6} + 16 x^{5} + 44 x^{4} + 80 x^{3} + 40 x^{2} + 148$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 8 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.76 |
$12$ |
$x^{12} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 24 x^{7} + 36 x^{6} + 32 x^{5} + 60 x^{4} + 64 x^{3} + 40 x^{2} + 48 x + 84$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 10$ |
$[6, 0]$ |
$[1, 1]$ |
