| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.22.1 |
$8$ |
$x^{8} + 16 x^{7} + 68 x^{6} + 24 x^{5} + 48 x^{4} + 128 x^{3} + 280 x^{2} + 144 x + 108$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + 8 t x + 12 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.10 |
$8$ |
$x^{8} - 8 x^{7} + 88 x^{6} - 96 x^{5} + 204 x^{4} - 240 x^{3} + 720 x^{2} + 900$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 12 x^{2} + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.100 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.101 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.102 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.103 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^3 : C_4 $ (as 8T19) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.104 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^3 : C_4 $ (as 8T19) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.105 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^3 : C_4 $ (as 8T19) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.106 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^3 : C_4 $ (as 8T19) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.107 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.108 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 12 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.109 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.11 |
$8$ |
$x^{8} + 16 x^{7} + 72 x^{6} + 80 x^{5} + 212 x^{4} + 224 x^{3} + 144 x^{2} + 160 x + 100$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(8 t + 8\right) x^{2} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.110 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.111 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.112 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.113 |
$8$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 10 x^{4} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.8.22.114 |
$8$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 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) |
$2$ |
$3$ |
$[3, 19/6, 19/6]$ |
$[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 2$ |
$[15, 14, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.12 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 52 x^{4} + 64 x^{3} + 208 x^{2} + 288 x + 516$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{2} + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.13 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 108 x^{4} + 64 x^{3} + 240 x^{2} + 352 x + 484$ |
$2$ |
$4$ |
$2$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{2} + 8 x + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$3$ |
$[2, 10/3, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 6$ |
$[15, 12, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.131 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.132 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.133 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 12 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.134 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.135 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.136 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 10$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.137 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.138 |
$8$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.139 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.14 |
$8$ |
$x^{8} + 4 x^{7} + 18 x^{6} + 56 x^{5} + 131 x^{4} + 200 x^{3} + 234 x^{2} + 316 x + 223$ |
$2$ |
$4$ |
$2$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2, 3, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.8.22.140 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.141 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.142 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 12 x^{4} + 4 x^{2} + 8 x + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.22.143 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$22$ |
$Q_8:S_4$ (as 8T40) |
$2$ |
$3$ |
$[8/3, 8/3, 7/2]$ |
$[4/3, 4/3, 8/3, 8/3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$[15, 10, 8, 0]$ |
$[1, 1]$ |
