| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.10.12.11 |
$10$ |
$x^{10} - 20 x^{7} + 10 x^{5} - 100 x^{4} - 100 x^{2} + 25$ |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.10.12.12 |
$10$ |
$x^{10} - 30 x^{7} + 10 x^{5} + 25 x^{4} - 150 x^{2} + 25$ |
$5$ |
$5$ |
$2$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.10.15.17 |
$10$ |
$x^{10} + 15 x^{8} + 5 x^{7} + 20 x^{6} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 5 x^{7} + 20 x^{6} + 5 x^{5} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.18 |
$10$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{6} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{6} + 5 x^{5} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.19 |
$10$ |
$x^{10} + 15 x^{8} + 10 x^{7} + 5 x^{6} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{8} + 10 x^{7} + 5 x^{6} + 5 x^{5} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.20 |
$10$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{6} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{6} + 5 x^{5} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.5 |
$10$ |
$x^{10} + 20 x^{8} + 15 x^{7} + 10 x^{6} + 5 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 15 x^{7} + 10 x^{6} + 5 x^{5} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.6 |
$10$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 10 x^{6} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 10 x^{6} + 15 x^{5} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.7 |
$10$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{6} + 5 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{6} + 5 x^{5} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.8 |
$10$ |
$x^{10} + 20 x^{8} + 5 x^{7} + 15 x^{6} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[7/4]$ |
$[5/4, 7/4]_{4}$ |
$t + 3$ |
$x^{10} + 20 x^{8} + 5 x^{7} + 15 x^{6} + 15 x^{5} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.16.27 |
$10$ |
$x^{10} - 10 x^{9} - 25 x^{8} + 10 x^{5} - 50 x^{4} + 25$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 5\right) x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
| 5.10.16.28 |
$10$ |
$x^{10} + 10 x^{9} - 25 x^{8} + 10 x^{5} + 50 x^{4} + 25$ |
$5$ |
$5$ |
$2$ |
$16$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 15\right) x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
| 5.10.19.10 |
$10$ |
$x^{10} + 15 x^{5} + 75 x^{3} + 50 x^{2} + 25 x + 30$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{5} + 75 x^{3} + 50 x^{2} + 25 x + 30$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.11 |
$10$ |
$x^{10} + 5 x^{5} + 50 x^{2} + 50 x + 55$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{5} + 50 x^{2} + 50 x + 55$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.12 |
$10$ |
$x^{10} + 15 x^{5} + 75 x^{2} + 25 x + 80$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{5} + 75 x^{2} + 25 x + 80$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.13 |
$10$ |
$x^{10} + 5 x^{5} + 100 x^{3} + 75 x^{2} + 50 x + 105$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{5} + 100 x^{3} + 75 x^{2} + 50 x + 105$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.14 |
$10$ |
$x^{10} + 15 x^{5} + 50 x^{3} + 100 x^{2} + 25 x + 5$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{5} + 50 x^{3} + 100 x^{2} + 25 x + 5$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.15 |
$10$ |
$x^{10} + 5 x^{5} + 75 x^{3} + 100 x^{2} + 50 x + 30$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{5} + 75 x^{3} + 100 x^{2} + 50 x + 30$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.6 |
$10$ |
$x^{10} + 15 x^{5} + 100 x^{3} + 25 x + 55$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{5} + 100 x^{3} + 25 x + 55$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.7 |
$10$ |
$x^{10} + 5 x^{5} + 50 x^{3} + 50 x + 80$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{5} + 50 x^{3} + 50 x + 80$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.8 |
$10$ |
$x^{10} + 15 x^{5} + 25 x^{3} + 25 x^{2} + 25 x + 105$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{5} + 25 x^{3} + 25 x^{2} + 25 x + 105$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.9 |
$10$ |
$x^{10} + 5 x^{5} + 25 x^{3} + 25 x^{2} + 50 x + 5$ |
$5$ |
$10$ |
$1$ |
$19$ |
$C_5^2 : C_4$ (as 10T10) |
$1$ |
$4$ |
$[9/4]$ |
$[7/4, 9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{5} + 25 x^{3} + 25 x^{2} + 50 x + 5$ |
$[10, 0]$ |
$[1, 1]$ |
