Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.6.10.1 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{2} + 4 x + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4$ (as 6T7) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{2} + 4 x + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.2 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{4} + 4 x + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4$ (as 6T7) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{4} + 4 x + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.3 |
$6$ |
$x^{6} + 2 x^{5} + 4 x + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4$ (as 6T8) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.4 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 4 x + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4$ (as 6T8) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 4 x + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.5 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4\times C_2$ (as 6T11) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.6 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{2} + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4\times C_2$ (as 6T11) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{2} + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.7 |
$6$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4\times C_2$ (as 6T11) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{3} + 2$ |
$[5, 0]$ |
$[1, 2]$ |
2.6.10.8 |
$6$ |
$x^{6} + 2 x^{5} + 2$ |
$2$ |
$6$ |
$1$ |
$10$ |
$S_4\times C_2$ (as 6T11) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{6} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 2]$ |