| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.16.19 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 14 x^{8} + 8 x^{6} + 4 x^{5} + 16 x^{4} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.20.16 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 24 x^{8} + 16 x^{7} + 40 x^{6} + 52 x^{4} + 24 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 4\right) x^{4} + \left(4 t + 6\right) x^{2} + 4 t + 2$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.52 |
$12$ |
$x^{12} - 2 x^{11} + 6 x^{10} + 24 x^{9} + 20 x^{8} + 16 x^{7} + 20 x^{6} - 4 x^{5} + 44 x^{4} + 48 x^{3} + 16 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(6 t + 4\right) x^{4} + 4 x^{3} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.22.18 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 20 x^{8} + 40 x^{7} + 40 x^{6} + 24 x^{5} + 124 x^{4} + 120 x^{3} + 48 x^{2} + 64 x + 172$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 4 x + 12 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.26 |
$12$ |
$x^{12} + 14 x^{11} + 93 x^{10} + 386 x^{9} + 1116 x^{8} + 2374 x^{7} + 3841 x^{6} + 4862 x^{5} + 4576 x^{4} + 2330 x^{3} - 131 x^{2} - 510 x + 129$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.31 |
$12$ |
$x^{12} - 4 x^{10} - 4 x^{9} + 28 x^{8} + 40 x^{7} - 40 x^{5} + 28 x^{4} + 56 x^{3} + 64 x^{2} + 32 x + 28$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 4 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.39 |
$12$ |
$x^{12} - 4 x^{7} + 4 x^{6} + 16 x^{2} - 8 x + 4$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x + 2$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.53 |
$12$ |
$x^{12} + 8 x^{11} + 14 x^{10} + 68 x^{8} + 20 x^{7} + 8 x^{6} + 136 x^{5} + 92 x^{4} + 48 x^{3} + 80 x^{2} + 40 x + 172$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + \left(6 t + 2\right) x^{4} + 4 x^{3} + 4 x^{2} + 4 t x + 12 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.61 |
$12$ |
$x^{12} + 8 x^{10} + 8 x^{9} + 28 x^{8} + 28 x^{7} + 44 x^{6} + 8 x^{5} + 60 x^{4} + 40 x^{3} + 64 x^{2} + 40 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t x + 8 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
