| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 23.8.0.1 |
$8$ |
$x^{8} + 3 x^{4} + 20 x^{3} + 5 x^{2} + 3 x + 5$ |
$23$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]^{8}$ |
$t^{8} + 3 t^{4} + 20 t^{3} + 5 t^{2} + 3 t + 5$ |
$x - 23$ |
$[0]$ |
$[]$ |
| 23.8.4.1 |
$8$ |
$x^{8} + 98 x^{6} + 38 x^{5} + 3331 x^{4} - 1634 x^{3} + 44919 x^{2} - 57494 x + 224528$ |
$23$ |
$2$ |
$4$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
| 23.8.4.2 |
$8$ |
$x^{8} + 1587 x^{4} - 231173 x^{2} + 1399205$ |
$23$ |
$2$ |
$4$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{2} + 23 t$ |
$[0]$ |
$[1]$ |
| 23.8.6.1 |
$8$ |
$x^{8} - 138 x^{4} - 217948$ |
$23$ |
$4$ |
$2$ |
$6$ |
$Q_8$ (as 8T5) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{4} + 46 t + 414$ |
$[0]$ |
$[1]$ |
| 23.8.6.2 |
$8$ |
$x^{8} + 84 x^{7} + 2666 x^{6} + 38304 x^{5} + 221137 x^{4} + 193452 x^{3} + 126128 x^{2} + 833532 x + 4272507$ |
$23$ |
$4$ |
$2$ |
$6$ |
$D_4$ (as 8T4) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{4} + 23$ |
$[0]$ |
$[1]$ |
| 23.8.6.3 |
$8$ |
$x^{8} - 483 x^{4} + 2645$ |
$23$ |
$4$ |
$2$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$t^{2} + 21 t + 5$ |
$x^{4} + 23 t$ |
$[0]$ |
$[1]$ |
| 23.8.7.1 |
$8$ |
$x^{8} + 23$ |
$23$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 18$ |
$x^{8} + 23$ |
$[0]$ |
$[2]$ |
| 23.8.7.2 |
$8$ |
$x^{8} + 115$ |
$23$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 18$ |
$x^{8} + 115$ |
$[0]$ |
$[2]$ |
