| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.12.17 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 4$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^4:C_6$ (as 8T33) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.8.12.18 |
$8$ |
$x^{8} - 2 x^{7} + 4 x^{6} + 8 x^{4} + 4 x^{3} + 28$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^4:C_6$ (as 8T33) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{2} + t + 1$ |
$x^{4} + 2 t x^{3} + 4 t + 6$ |
$[3, 3, 0]$ |
$[3]$ |
| 2.8.20.77 |
$8$ |
$x^{8} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[2, 3, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 6$ |
$[13, 10, 4, 0]$ |
$[3, 1]$ |
| 2.8.20.78 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[2, 3, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 6$ |
$[13, 10, 4, 0]$ |
$[3, 1]$ |
| 2.8.20.79 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[2, 3, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 2$ |
$[13, 10, 4, 0]$ |
$[3, 1]$ |
| 2.8.20.80 |
$8$ |
$x^{8} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[2, 3, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 2 x^{4} + 4 x^{2} + 2$ |
$[13, 10, 4, 0]$ |
$[3, 1]$ |
| 2.8.24.57 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x + 10$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.58 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{2} + 8 x + 2$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.59 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x + 2$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.60 |
$8$ |
$x^{8} + 4 x^{6} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x + 2$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.61 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{3} + 8 x + 10$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.62 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x + 2$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.63 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x + 10$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
| 2.8.24.64 |
$8$ |
$x^{8} + 4 x^{6} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$24$ |
$C_2^4:C_6$ (as 8T33) |
$3$ |
$1$ |
$[3, 7/2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x + 10$ |
$[17, 14, 8, 0]$ |
$[3, 1]$ |
