Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.22.51 |
$8$ |
$x^{8} + 16 x^{7} + 64 x^{6} + 24 x^{4} + 192 x^{3} + 156$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.22.52 |
$8$ |
$x^{8} - 8 x^{7} + 76 x^{6} + 8 x^{5} + 164 x^{4} - 16 x^{3} + 424 x^{2} + 304 x + 724$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
2.8.24.65 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.24.67 |
$8$ |
$x^{8} + 12 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$24$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[2, 3, 4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.1 |
$8$ |
$x^{8} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 18$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 18$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.115 |
$8$ |
$x^{8} + 4 x^{6} + 18 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 18 x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.116 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.2 |
$8$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 18$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 18$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.41 |
$8$ |
$x^{8} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.42 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 18$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 18$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.83 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.27.84 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$27$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[2, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
2.8.28.101 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.104 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.65 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{2} + 10$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.66 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 16 x^{2} + 18$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 16 x^{2} + 18$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.71 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 26$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 26$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.72 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.97 |
$8$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 10$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 10$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.28.99 |
$8$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x + 18$ |
$2$ |
$8$ |
$1$ |
$28$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 7/2, 9/2]$ |
$[2, 3, 7/2, 9/2]$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x + 18$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.13 |
$8$ |
$x^{8} + 18$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.14 |
$8$ |
$x^{8} + 2$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.15 |
$8$ |
$x^{8} + 34$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.16 |
$8$ |
$x^{8} + 50$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.169 |
$8$ |
$x^{8} + 8 x^{4} + 24 x^{2} + 16 x + 26$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[3, 4, 5]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{4} + 24 x^{2} + 16 x + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.171 |
$8$ |
$x^{8} + 24 x^{4} + 24 x^{2} + 16 x + 26$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[3, 4, 5]^{2}$ |
$t + 1$ |
$x^{8} + 24 x^{4} + 24 x^{2} + 16 x + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.174 |
$8$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 34$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.175 |
$8$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 50$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.177 |
$8$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 2$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.180 |
$8$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 18$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2, 3, 4, 5]$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.233 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 18$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[3, 4, 5]^{2}$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
2.8.31.235 |
$8$ |
$x^{8} + 8 x^{2} + 16 x + 18$ |
$2$ |
$8$ |
$1$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[3, 4, 5]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{2} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
7.8.7.1 |
$8$ |
$x^{8} + 7$ |
$7$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 4$ |
$x^{8} + 7$ |
$[0]$ |
$[2]$ |
7.8.7.2 |
$8$ |
$x^{8} + 21$ |
$7$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 4$ |
$x^{8} + 21$ |
$[0]$ |
$[2]$ |
23.8.7.1 |
$8$ |
$x^{8} + 23$ |
$23$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 18$ |
$x^{8} + 23$ |
$[0]$ |
$[2]$ |
23.8.7.2 |
$8$ |
$x^{8} + 115$ |
$23$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 18$ |
$x^{8} + 115$ |
$[0]$ |
$[2]$ |
31.8.7.1 |
$8$ |
$x^{8} + 31$ |
$31$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 28$ |
$x^{8} + 31$ |
$[0]$ |
$[2]$ |
31.8.7.2 |
$8$ |
$x^{8} + 93$ |
$31$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 28$ |
$x^{8} + 93$ |
$[0]$ |
$[2]$ |
47.8.7.1 |
$8$ |
$x^{8} + 47$ |
$47$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 42$ |
$x^{8} + 47$ |
$[0]$ |
$[2]$ |
47.8.7.2 |
$8$ |
$x^{8} + 235$ |
$47$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 42$ |
$x^{8} + 235$ |
$[0]$ |
$[2]$ |
71.8.7.1 |
$8$ |
$x^{8} + 71$ |
$71$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 64$ |
$x^{8} + 71$ |
$[0]$ |
$[2]$ |
71.8.7.2 |
$8$ |
$x^{8} + 497$ |
$71$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 64$ |
$x^{8} + 497$ |
$[0]$ |
$[2]$ |
79.8.7.1 |
$8$ |
$x^{8} + 79$ |
$79$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 76$ |
$x^{8} + 79$ |
$[0]$ |
$[2]$ |
79.8.7.2 |
$8$ |
$x^{8} + 237$ |
$79$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 76$ |
$x^{8} + 237$ |
$[0]$ |
$[2]$ |
103.8.7.1 |
$8$ |
$x^{8} + 103$ |
$103$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 98$ |
$x^{8} + 103$ |
$[0]$ |
$[2]$ |
103.8.7.2 |
$8$ |
$x^{8} + 309$ |
$103$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 98$ |
$x^{8} + 309$ |
$[0]$ |
$[2]$ |
127.8.7.1 |
$8$ |
$x^{8} + 127$ |
$127$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 124$ |
$x^{8} + 127$ |
$[0]$ |
$[2]$ |
127.8.7.2 |
$8$ |
$x^{8} + 381$ |
$127$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 124$ |
$x^{8} + 381$ |
$[0]$ |
$[2]$ |
151.8.7.1 |
$8$ |
$x^{8} + 151$ |
$151$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 145$ |
$x^{8} + 151$ |
$[0]$ |
$[2]$ |
151.8.7.2 |
$8$ |
$x^{8} + 453$ |
$151$ |
$8$ |
$1$ |
$7$ |
$D_{8}$ (as 8T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$t + 145$ |
$x^{8} + 453$ |
$[0]$ |
$[2]$ |