Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.8.20.85 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 2$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.86 |
$8$ |
$x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 14$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 14$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.87 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.88 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 6$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.89 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 8 x^{2} + 2$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.90 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 12 x^{2} + 2$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.91 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 14$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 14$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
2.8.20.92 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x + 6$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
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) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{4} + 12 x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.22.110 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$22$ |
$C_2^2 \wr C_2$ (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) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
2.8.26.17 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.18 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.19 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.20 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.21 |
$8$ |
$x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.22 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.23 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.24 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.25 |
$8$ |
$x^{8} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.26 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.27 |
$8$ |
$x^{8} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.28 |
$8$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.29 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 26$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 26$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.30 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.31 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
2.8.26.32 |
$8$ |
$x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 18$ |
$2$ |
$8$ |
$1$ |
$26$ |
$C_2^2 \wr C_2$ (as 8T18) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 18$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |