Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.10.12.1 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.2 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.3 |
$10$ |
$x^{10} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
2.10.12.4 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |