| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 13.10.0.1 |
$10$ |
$x^{10} + 7 x^{5} + 5 x^{4} + 8 x^{3} + x^{2} + x + 2$ |
$13$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + 7 t^{5} + 5 t^{4} + 8 t^{3} + t^{2} + t + 2$ |
$x - 13$ |
$[0]$ |
$[]$ |
| 13.10.5.1 |
$10$ |
$x^{10} + 650 x^{9} + 169065 x^{8} + 22003800 x^{7} + 1434642698 x^{6} + 37701182242 x^{5} + 18651037600 x^{4} + 3808243140 x^{3} + 6315953361 x^{2} + 164195122608 x + 421659070668$ |
$13$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 4 t + 11$ |
$x^{2} + 130 x + 13$ |
$[0]$ |
$[1]$ |
| 13.10.5.2 |
$10$ |
$x^{10} + 114244 x^{2} - 4084223$ |
$13$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 4 t + 11$ |
$x^{2} + 13 t$ |
$[0]$ |
$[1]$ |
| 13.10.8.1 |
$10$ |
$x^{10} + 60 x^{9} + 1450 x^{8} + 17760 x^{7} + 112360 x^{6} + 319418 x^{5} + 225500 x^{4} + 89240 x^{3} + 226880 x^{2} + 1274440 x + 3013497$ |
$13$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 12 t + 2$ |
$x^{5} + 13$ |
$[0]$ |
$[2]$ |
| 13.10.9.1 |
$10$ |
$x^{10} + 13$ |
$13$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 11$ |
$x^{10} + 13$ |
$[0]$ |
$[4]$ |
| 13.10.9.2 |
$10$ |
$x^{10} + 26$ |
$13$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 11$ |
$x^{10} + 26$ |
$[0]$ |
$[4]$ |
