| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.6.6.3 |
$6$ |
$x^{6} + 18 x^{5} + 120 x^{4} + 386 x^{3} + 723 x^{2} + 732 x + 305$ |
$3$ |
$3$ |
$2$ |
$6$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 x^{2} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.6.6.4 |
$6$ |
$x^{6} + 48 x^{4} + 6 x^{3} + 36 x^{2} + 36 x + 9$ |
$3$ |
$3$ |
$2$ |
$6$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.6.7.2 |
$6$ |
$x^{6} + 3 x^{2} + 6$ |
$3$ |
$6$ |
$1$ |
$7$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{2} + 6$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.6.7.5 |
$6$ |
$x^{6} + 6 x^{2} + 3$ |
$3$ |
$6$ |
$1$ |
$7$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.6.9.12 |
$6$ |
$x^{6} + 3 x^{4} + 3$ |
$3$ |
$6$ |
$1$ |
$9$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.9.4 |
$6$ |
$x^{6} + 6 x^{4} + 6$ |
$3$ |
$6$ |
$1$ |
$9$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.10.1 |
$6$ |
$x^{6} + 18 x^{4} + 6 x^{3} + 162 x^{2} + 216 x + 90$ |
$3$ |
$3$ |
$2$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(9 t + 18\right) x + 9 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.6.10.2 |
$6$ |
$x^{6} - 36 x^{4} - 12 x^{3} + 648 x^{2} + 864 x + 360$ |
$3$ |
$3$ |
$2$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 18 t x + 18 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.6.10.3 |
$6$ |
$x^{6} + 6 x^{5} + 36 x^{4} + 128 x^{3} + 297 x^{2} + 474 x + 482$ |
$3$ |
$3$ |
$2$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 9 x + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.6.11.1 |
$6$ |
$x^{6} + 18 x^{2} + 15$ |
$3$ |
$6$ |
$1$ |
$11$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 18 x^{2} + 15$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.6.11.2 |
$6$ |
$x^{6} + 9 x^{2} + 24$ |
$3$ |
$6$ |
$1$ |
$11$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 9 x^{2} + 24$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.6.11.3 |
$6$ |
$x^{6} + 6$ |
$3$ |
$6$ |
$1$ |
$11$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 6$ |
$[6, 0]$ |
$[2, 1]$ |
