| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 11.8.0.1 |
$8$ |
$x^{8} + 7 x^{4} + 7 x^{3} + x^{2} + 7 x + 2$ |
$11$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]^{8}$ |
$t^{8} + 7 t^{4} + 7 t^{3} + t^{2} + 7 t + 2$ |
$x - 11$ |
$[0]$ |
$[]$ |
| 11.8.4.1 |
$8$ |
$x^{8} + 60 x^{6} + 20 x^{5} + 970 x^{4} - 280 x^{3} + 4664 x^{2} - 5460 x + 2325$ |
$11$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{2} + 11$ |
$[0]$ |
$[1]$ |
| 11.8.4.2 |
$8$ |
$x^{8} + 968 x^{4} - 13310 x^{2} + 29282$ |
$11$ |
$2$ |
$4$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{2} + 11 t$ |
$[0]$ |
$[1]$ |
| 11.8.6.1 |
$8$ |
$x^{8} - 110 x^{4} - 16819$ |
$11$ |
$4$ |
$2$ |
$6$ |
$Q_8$ (as 8T5) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{4} + 44 t + 99$ |
$[0]$ |
$[1]$ |
| 11.8.6.2 |
$8$ |
$x^{8} + 28 x^{7} + 302 x^{6} + 1540 x^{5} + 3623 x^{4} + 3388 x^{3} + 4178 x^{2} + 13468 x + 22324$ |
$11$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{4} + 11$ |
$[0]$ |
$[1]$ |
| 11.8.6.3 |
$8$ |
$x^{8} - 165 x^{4} - 4356$ |
$11$ |
$4$ |
$2$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$t^{2} + 7 t + 2$ |
$x^{4} + 33 t + 33$ |
$[0]$ |
$[1]$ |
| 11.8.7.1 |
$8$ |
$x^{8} + 11$ |
$11$ |
$8$ |
$1$ |
$7$ |
$QD_{16}$ (as 8T8) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 9$ |
$x^{8} + 11$ |
$[0]$ |
$[2]$ |
| 11.8.7.2 |
$8$ |
$x^{8} + 22$ |
$11$ |
$8$ |
$1$ |
$7$ |
$QD_{16}$ (as 8T8) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 9$ |
$x^{8} + 22$ |
$[0]$ |
$[2]$ |
