| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.10.14.1 |
$10$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.2 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.3 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.4 |
$10$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.5 |
$10$ |
$x^{10} + 2 x^{5} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.6 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.7 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.8 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{4} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{4} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
