| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 17.10.0.1 |
$10$ |
$x^{10} + 13 x^{5} + 6 x^{4} + 5 x^{3} + 9 x^{2} + 12 x + 3$ |
$17$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + 13 t^{5} + 6 t^{4} + 5 t^{3} + 9 t^{2} + 12 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
| 17.10.5.1 |
$10$ |
$x^{10} + 765 x^{9} + 234175 x^{8} + 35867790 x^{7} + 2751847887 x^{6} + 85060199629 x^{5} + 46781658675 x^{4} + 10404827560 x^{3} + 4386754121 x^{2} + 122151890859 x + 1178806975473$ |
$17$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + t + 14$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 17.10.5.2 |
$10$ |
$x^{10} + 83521 x^{2} - 19877998$ |
$17$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + t + 14$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.10.8.1 |
$10$ |
$x^{10} + 80 x^{9} + 2575 x^{8} + 41920 x^{7} + 350810 x^{6} + 1298690 x^{5} + 1053790 x^{4} + 419780 x^{3} + 741365 x^{2} + 5317450 x + 16794084$ |
$17$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 16 t + 3$ |
$x^{5} + 17$ |
$[0]$ |
$[2]$ |
| 17.10.9.1 |
$10$ |
$x^{10} + 17$ |
$17$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 14$ |
$x^{10} + 17$ |
$[0]$ |
$[4]$ |
| 17.10.9.2 |
$10$ |
$x^{10} + 51$ |
$17$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 14$ |
$x^{10} + 51$ |
$[0]$ |
$[4]$ |
