| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 17.8.0.1 |
$8$ |
$x^{8} + 11 x^{4} + 12 x^{3} + 6 x + 3$ |
$17$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]^{8}$ |
$t^{8} + 11 t^{4} + 12 t^{3} + 6 t + 3$ |
$x - 17$ |
$[0]$ |
$[]$ |
| 17.8.4.1 |
$8$ |
$x^{8} + 612 x^{7} + 140536 x^{6} + 14363966 x^{5} + 553913435 x^{4} + 345855654 x^{3} + 4032327212 x^{2} + 6379401496 x + 2294776272$ |
$17$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 17.8.4.2 |
$8$ |
$x^{8} + 2023 x^{4} - 49130 x^{2} + 250563$ |
$17$ |
$2$ |
$4$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.8.6.1 |
$8$ |
$x^{8} + 64 x^{7} + 1548 x^{6} + 16960 x^{5} + 74840 x^{4} + 51968 x^{3} + 39432 x^{2} + 270464 x + 1062564$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
| 17.8.6.2 |
$8$ |
$x^{8} + 204 x^{4} - 7225$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t + 238$ |
$[0]$ |
$[1]$ |
| 17.8.6.3 |
$8$ |
$x^{8} - 272 x^{4} + 867$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.8.6.4 |
$8$ |
$x^{8} - 3604 x^{4} - 719321$ |
$17$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 255 t + 238$ |
$[0]$ |
$[1]$ |
| 17.8.7.1 |
$8$ |
$x^{8} + 68$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 68$ |
$[0]$ |
$[1]$ |
| 17.8.7.2 |
$8$ |
$x^{8} + 136$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 136$ |
$[0]$ |
$[1]$ |
| 17.8.7.3 |
$8$ |
$x^{8} + 17$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 17$ |
$[0]$ |
$[1]$ |
| 17.8.7.4 |
$8$ |
$x^{8} + 34$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 34$ |
$[0]$ |
$[1]$ |
| 17.8.7.5 |
$8$ |
$x^{8} + 119$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 119$ |
$[0]$ |
$[1]$ |
| 17.8.7.6 |
$8$ |
$x^{8} + 102$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 102$ |
$[0]$ |
$[1]$ |
| 17.8.7.7 |
$8$ |
$x^{8} + 51$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 51$ |
$[0]$ |
$[1]$ |
| 17.8.7.8 |
$8$ |
$x^{8} + 85$ |
$17$ |
$8$ |
$1$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}$ |
$t + 14$ |
$x^{8} + 85$ |
$[0]$ |
$[1]$ |
