| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.6.9.1 |
$6$ |
$x^{6} + 3 x^{4} + 15$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{4} + 15$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.10 |
$6$ |
$x^{6} + 6 x^{4} + 3$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 6 x^{4} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.11 |
$6$ |
$x^{6} + 6 x^{4} + 12$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 6 x^{4} + 12$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.12 |
$6$ |
$x^{6} + 3 x^{4} + 3$ |
$3$ |
$6$ |
$1$ |
$9$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.9.13 |
$6$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 21$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.14 |
$6$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 12$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 12$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.15 |
$6$ |
$x^{6} + 6 x^{5} + 6 x^{4} + 3$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 6 x^{5} + 6 x^{4} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.16 |
$6$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 12$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 12$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.9.2 |
$6$ |
$x^{6} + 3 x^{4} + 6$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{4} + 6$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.3 |
$6$ |
$x^{6} + 3 x^{4} + 24$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{4} + 24$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.4 |
$6$ |
$x^{6} + 6 x^{4} + 6$ |
$3$ |
$6$ |
$1$ |
$9$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.9.5 |
$6$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 6$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 6$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.6 |
$6$ |
$x^{6} + 6 x^{5} + 3 x^{4} + 24$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 6 x^{5} + 3 x^{4} + 24$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.7 |
$6$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 15$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3\times C_3$ (as 6T5) |
$1$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 15$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.6.9.8 |
$6$ |
$x^{6} + 6 x^{5} + 6 x^{4} + 15$ |
$3$ |
$6$ |
$1$ |
$9$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 1$ |
$x^{6} + 6 x^{5} + 6 x^{4} + 15$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.6.9.9 |
$6$ |
$x^{6} + 6 x^{4} + 21$ |
$3$ |
$6$ |
$1$ |
$9$ |
$C_6$ (as 6T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 1$ |
$x^{6} + 6 x^{4} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
