| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.16.63 |
$8$ |
$x^{8} + 2 x^{4} + 4 x + 6$ |
$2$ |
$8$ |
$1$ |
$16$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 7/3, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x + 6$ |
$[9, 9, 4, 0]$ |
$[1, 1]$ |
| 2.8.16.64 |
$8$ |
$x^{8} + 2 x^{4} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$16$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 7/3, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x + 2$ |
$[9, 9, 4, 0]$ |
$[1, 1]$ |
| 2.8.18.71 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[11, 10, 4, 0]$ |
$[1, 1]$ |
| 2.8.18.72 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$18$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$[11, 10, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.115 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 10$ |
$[15, 14, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.116 |
$8$ |
$x^{8} + 4 x^{7} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2$ |
$[15, 15, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.117 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ |
$[15, 15, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.118 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 10$ |
$[15, 14, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.119 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2$ |
$[15, 14, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.120 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 2$ |
$[15, 14, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.121 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 10$ |
$[15, 15, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.122 |
$8$ |
$x^{8} + 4 x^{7} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10$ |
$[15, 15, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.123 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.124 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 2$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.125 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{2} + 2$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.126 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.127 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x + 2$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.128 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 2$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.129 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{2} + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.130 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.26.49 |
$8$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.50 |
$8$ |
$x^{8} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{3} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.51 |
$8$ |
$x^{8} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.52 |
$8$ |
$x^{8} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{3} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.53 |
$8$ |
$x^{8} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.54 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.55 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.56 |
$8$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.57 |
$8$ |
$x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.58 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.59 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.60 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.61 |
$8$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 8 x^{3} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.62 |
$8$ |
$x^{8} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{3} + 8 x^{2} + 10$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.63 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
| 2.8.26.64 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$2$ |
$3$ |
$[3, 23/6, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 2$ |
$[19, 16, 8, 0]$ |
$[1, 1]$ |
