| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.10.0.1 |
$10$ |
$x^{10} + 3 x^{5} + 3 x^{4} + 2 x^{3} + 4 x^{2} + x + 2$ |
$5$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + 3 t^{5} + 3 t^{4} + 2 t^{3} + 4 t^{2} + t + 2$ |
$x - 5$ |
$[0]$ |
$[]$ |
| 5.10.5.1 |
$10$ |
$x^{10} + 100 x^{9} + 4025 x^{8} + 82000 x^{7} + 860258 x^{6} + 4015486 x^{5} + 4317350 x^{4} + 2373700 x^{3} + 3853141 x^{2} + 15123594 x + 12051954$ |
$5$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 4 t + 3$ |
$x^{2} + 20 x + 5$ |
$[0]$ |
$[1]$ |
| 5.10.5.2 |
$10$ |
$x^{10} + 2500 x^{2} - 9375$ |
$5$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 4 t + 3$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
| 5.10.16.10 |
$10$ |
$x^{10} + 40 x^{9} + 400 x^{8} - 90 x^{5} - 1800 x^{4} - 2975$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_{10}$ (as 10T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{4} + 50 t + 55$ |
$[4, 0]$ |
$[1]$ |
| 5.10.16.11 |
$10$ |
$x^{10} + 40 x^{9} + 400 x^{8} - 40 x^{5} - 800 x^{4} - 4600$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_{10}$ (as 10T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{4} + 50 t + 80$ |
$[4, 0]$ |
$[1]$ |
| 5.10.16.7 |
$10$ |
$x^{10} + 40 x^{9} + 400 x^{8} + 10 x^{5} + 200 x^{4} - 1225$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_{10}$ (as 10T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{4} + 25 t + 55$ |
$[4, 0]$ |
$[1]$ |
| 5.10.16.8 |
$10$ |
$x^{10} + 40 x^{9} + 400 x^{8} - 190 x^{5} - 3800 x^{4} + 4025$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_{10}$ (as 10T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{4} + 50 t + 5$ |
$[4, 0]$ |
$[1]$ |
| 5.10.16.9 |
$10$ |
$x^{10} + 40 x^{9} + 400 x^{8} - 140 x^{5} - 2800 x^{4} - 100$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_{10}$ (as 10T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{4} + 50 t + 30$ |
$[4, 0]$ |
$[1]$ |
| 5.10.17.1 |
$10$ |
$x^{10} + 20 x^{8} + 5$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 5$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.2 |
$10$ |
$x^{10} + 20 x^{8} + 80$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 80$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.25 |
$10$ |
$x^{10} + 15 x^{8} + 60$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 60$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.26 |
$10$ |
$x^{10} + 15 x^{8} + 85$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 85$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.27 |
$10$ |
$x^{10} + 15 x^{8} + 10$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 10$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.28 |
$10$ |
$x^{10} + 15 x^{8} + 110$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 110$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.29 |
$10$ |
$x^{10} + 15 x^{8} + 35$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 35$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.3 |
$10$ |
$x^{10} + 20 x^{8} + 30$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 30$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.4 |
$10$ |
$x^{10} + 20 x^{8} + 105$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 105$ |
$[8, 0]$ |
$[1, 1]$ |
| 5.10.17.5 |
$10$ |
$x^{10} + 20 x^{8} + 55$ |
$5$ |
$10$ |
$1$ |
$17$ |
$C_{10}$ (as 10T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 55$ |
$[8, 0]$ |
$[1, 1]$ |
