| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 13.8.0.1 |
$8$ |
$x^{8} + 8 x^{4} + 12 x^{3} + 2 x^{2} + 3 x + 2$ |
$13$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]^{8}$ |
$t^{8} + 8 t^{4} + 12 t^{3} + 2 t^{2} + 3 t + 2$ |
$x - 13$ |
$[0]$ |
$[]$ |
| 13.8.4.1 |
$8$ |
$x^{8} + 520 x^{7} + 101458 x^{6} + 8810644 x^{5} + 288610205 x^{4} + 142111548 x^{3} + 982314112 x^{2} + 3617879976 x + 920156436$ |
$13$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 12 t + 2$ |
$x^{2} + 130 x + 13$ |
$[0]$ |
$[1]$ |
| 13.8.4.2 |
$8$ |
$x^{8} + 507 x^{4} - 26364 x^{2} + 57122$ |
$13$ |
$2$ |
$4$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 12 t + 2$ |
$x^{2} + 13 t$ |
$[0]$ |
$[1]$ |
| 13.8.6.1 |
$8$ |
$x^{8} + 48 x^{7} + 872 x^{6} + 7200 x^{5} + 24242 x^{4} + 15024 x^{3} + 14408 x^{2} + 86496 x + 254881$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13$ |
$[0]$ |
$[1]$ |
| 13.8.6.2 |
$8$ |
$x^{8} + 130 x^{4} - 1521$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13 t + 143$ |
$[0]$ |
$[1]$ |
| 13.8.6.3 |
$8$ |
$x^{8} - 1586 x^{4} - 198575$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 156 t + 143$ |
$[0]$ |
$[1]$ |
| 13.8.6.4 |
$8$ |
$x^{8} - 156 x^{4} + 338$ |
$13$ |
$4$ |
$2$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13 t$ |
$[0]$ |
$[1]$ |
| 13.8.7.1 |
$8$ |
$x^{8} + 52$ |
$13$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 11$ |
$x^{8} + 52$ |
$[0]$ |
$[2]$ |
| 13.8.7.2 |
$8$ |
$x^{8} + 13$ |
$13$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 11$ |
$x^{8} + 13$ |
$[0]$ |
$[2]$ |
| 13.8.7.3 |
$8$ |
$x^{8} + 26$ |
$13$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 11$ |
$x^{8} + 26$ |
$[0]$ |
$[2]$ |
| 13.8.7.4 |
$8$ |
$x^{8} + 91$ |
$13$ |
$8$ |
$1$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 11$ |
$x^{8} + 91$ |
$[0]$ |
$[2]$ |
