| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.10.10.15 |
$10$ |
$x^{10} + 5 x + 5$ |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
| 5.10.10.16 |
$10$ |
$x^{10} + 10 x + 5$ |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
| 5.10.10.17 |
$10$ |
$x^{10} + 5 x + 10$ |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x + 10$ |
$[1, 0]$ |
$[1, 1]$ |
| 5.10.10.18 |
$10$ |
$x^{10} + 10 x + 10$ |
$5$ |
$10$ |
$1$ |
$10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x + 10$ |
$[1, 0]$ |
$[1, 1]$ |
| 5.10.12.15 |
$10$ |
$x^{10} + 5 x^{3} + 5$ |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8]$ |
$[11/8, 11/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
| 5.10.12.16 |
$10$ |
$x^{10} + 10 x^{3} + 10$ |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8]$ |
$[11/8, 11/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{3} + 10$ |
$[3, 0]$ |
$[1, 1]$ |
| 5.10.12.17 |
$10$ |
$x^{10} + 10 x^{3} + 5$ |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8]$ |
$[11/8, 11/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
| 5.10.12.18 |
$10$ |
$x^{10} + 5 x^{3} + 10$ |
$5$ |
$10$ |
$1$ |
$12$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[11/8]$ |
$[11/8, 11/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{3} + 10$ |
$[3, 0]$ |
$[1, 1]$ |
| 5.10.16.29 |
$10$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 15 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.30 |
$10$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 15 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.31 |
$10$ |
$x^{10} + 10 x^{7} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.32 |
$10$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 5 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.33 |
$10$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 5 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 5 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.34 |
$10$ |
$x^{10} + 5 x^{7} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.35 |
$10$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 20 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 20 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.36 |
$10$ |
$x^{10} + 5 x^{7} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{7} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.37 |
$10$ |
$x^{10} + 10 x^{7} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{7} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.38 |
$10$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 5 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.39 |
$10$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 5 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.40 |
$10$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 15 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 15 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.41 |
$10$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 15 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 15 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.42 |
$10$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 10 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 10 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.43 |
$10$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 10 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 10 x^{7} + 10 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.44 |
$10$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 20 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.45 |
$10$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{5} + 10$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{5} + 10$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.46 |
$10$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{8} + 20 x^{7} + 15 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.47 |
$10$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 15 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 15 x^{7} + 15 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.16.48 |
$10$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{5} + 5$ |
$5$ |
$10$ |
$1$ |
$16$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[15/8]$ |
$[15/8, 15/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{8} + 20 x^{7} + 5 x^{5} + 5$ |
$[7, 0]$ |
$[1, 1]$ |
| 5.10.18.16 |
$10$ |
$x^{10} + 10 x^{9} + 5$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 5$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.17 |
$10$ |
$x^{10} + 10 x^{9} + 25 x^{2} + 100 x + 55$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 25 x^{2} + 100 x + 55$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.18 |
$10$ |
$x^{10} + 10 x^{9} + 50 x^{2} + 75 x + 105$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 50 x^{2} + 75 x + 105$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.19 |
$10$ |
$x^{10} + 10 x^{9} + 75 x^{2} + 50 x + 30$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 75 x^{2} + 50 x + 30$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.20 |
$10$ |
$x^{10} + 10 x^{9} + 100 x^{2} + 25 x + 80$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 100 x^{2} + 25 x + 80$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.21 |
$10$ |
$x^{10} + 5 x^{9} + 25 x^{2} + 50 x + 55$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 25 x^{2} + 50 x + 55$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.22 |
$10$ |
$x^{10} + 5 x^{9} + 50 x^{2} + 100 x + 105$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 50 x^{2} + 100 x + 105$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.23 |
$10$ |
$x^{10} + 5 x^{9} + 75 x^{2} + 25 x + 30$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 75 x^{2} + 25 x + 30$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.24 |
$10$ |
$x^{10} + 5 x^{9} + 100 x^{2} + 75 x + 80$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 100 x^{2} + 75 x + 80$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.25 |
$10$ |
$x^{10} + 5 x^{9} + 10$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 10$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.26 |
$10$ |
$x^{10} + 5 x^{9} + 50 x^{2} + 100 x + 85$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 50 x^{2} + 100 x + 85$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.27 |
$10$ |
$x^{10} + 5 x^{9} + 100 x^{2} + 75 x + 35$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 100 x^{2} + 75 x + 35$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.28 |
$10$ |
$x^{10} + 5 x^{9} + 25 x^{2} + 50 x + 110$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 25 x^{2} + 50 x + 110$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.29 |
$10$ |
$x^{10} + 5 x^{9} + 5$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 5$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.30 |
$10$ |
$x^{10} + 5 x^{9} + 75 x^{2} + 25 x + 60$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 5 x^{9} + 75 x^{2} + 25 x + 60$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.31 |
$10$ |
$x^{10} + 10 x^{9} + 10$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 10$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.32 |
$10$ |
$x^{10} + 10 x^{9} + 50 x^{2} + 75 x + 85$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 50 x^{2} + 75 x + 85$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.33 |
$10$ |
$x^{10} + 10 x^{9} + 100 x^{2} + 25 x + 35$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 100 x^{2} + 25 x + 35$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.34 |
$10$ |
$x^{10} + 10 x^{9} + 25 x^{2} + 100 x + 110$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 25 x^{2} + 100 x + 110$ |
$[9, 0]$ |
$[1, 1]$ |
| 5.10.18.35 |
$10$ |
$x^{10} + 10 x^{9} + 75 x^{2} + 50 x + 60$ |
$5$ |
$10$ |
$1$ |
$18$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$2$ |
$8$ |
$[17/8]$ |
$[17/8, 17/8]_{8}^{2}$ |
$t + 3$ |
$x^{10} + 10 x^{9} + 75 x^{2} + 50 x + 60$ |
$[9, 0]$ |
$[1, 1]$ |
