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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.16.10 $x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} - 12 x^{4} + 8 x^{3} + 52 x^{2} + 72 x + 108$ $2$ $4$ $2$ $16$ $D_4\times C_2$ (as 8T9) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 12 t + 6$
2.8.16.11 $x^{8} + 2 x^{6} - 4 x^{5} + 20 x^{4} + 8 x^{3} + 44 x^{2} - 8 x + 76$ $2$ $4$ $2$ $16$ $D_4\times C_2$ (as 8T9) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(2 t + 2\right) x^{2} + 4 t x + 4 t + 10$
2.8.16.13 $x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} - 8 x^{4} + 24 x^{3} + 20 x^{2} - 8 x + 4$ $2$ $4$ $2$ $16$ $D_4\times C_2$ (as 8T9) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 2$
2.8.16.16 $x^{8} + 8 x^{7} + 26 x^{6} + 36 x^{5} + 40 x^{4} + 104 x^{3} + 156 x^{2} - 56 x + 196$ $2$ $4$ $2$ $16$ $D_4\times C_2$ (as 8T9) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 6\right) x^{2} + 4 t x + 14$
2.8.18.1 $x^{8} + 8 x^{7} + 40 x^{6} + 112 x^{5} + 232 x^{4} + 240 x^{3} + 256 x^{2} + 96 x + 84$ $2$ $4$ $2$ $18$ $D_4\times C_2$ (as 8T9) $[2, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(4 t + 14\right) x^{2} + 8 x + 8 t + 10$
2.8.18.2 $x^{8} + 4 x^{7} + 38 x^{6} + 116 x^{5} + 409 x^{4} + 816 x^{3} + 1332 x^{2} + 1260 x + 441$ $2$ $4$ $2$ $18$ $D_4\times C_2$ (as 8T9) $[2, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 14 x^{2} + 8 x + 14$
2.8.18.4 $x^{8} - 4 x^{7} + 40 x^{6} - 24 x^{5} + 168 x^{4} - 24 x^{3} + 144 x^{2} + 36$ $2$ $4$ $2$ $18$ $D_4\times C_2$ (as 8T9) $[2, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(4 t + 14\right) x^{2} + 6$
2.8.18.53 $x^{8} + 2 x^{6} + 4 x^{3} + 2$ $2$ $8$ $1$ $18$ $D_4\times C_2$ (as 8T9) $[2, 2, 3]$ $[2, 2, 3]^{2}$ $t + 1$ $x^{8} + 2 x^{6} + 4 x^{3} + 2$
2.8.18.54 $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ $2$ $8$ $1$ $18$ $D_4\times C_2$ (as 8T9) $[2, 2, 3]$ $[2, 2, 3]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$
2.8.18.55 $x^{8} + 2 x^{6} + 4 x^{3} + 10$ $2$ $8$ $1$ $18$ $D_4\times C_2$ (as 8T9) $[2, 2, 3]$ $[2, 2, 3]^{2}$ $t + 1$ $x^{8} + 2 x^{6} + 4 x^{3} + 10$
2.8.18.56 $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$ $2$ $8$ $1$ $18$ $D_4\times C_2$ (as 8T9) $[2, 2, 3]$ $[2, 2, 3]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$
2.8.18.7 $x^{8} + 4 x^{7} + 22 x^{6} + 52 x^{5} + 137 x^{4} + 192 x^{3} + 220 x^{2} + 132 x + 129$ $2$ $4$ $2$ $18$ $D_4\times C_2$ (as 8T9) $[2, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 6 x^{2} + 14$
2.8.20.1 $x^{8} + 8 x^{7} + 36 x^{6} + 80 x^{5} + 104 x^{4} - 32 x^{3} - 8 x^{2} + 124$ $2$ $4$ $2$ $20$ $D_4\times C_2$ (as 8T9) $[3, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(4 t + 12\right) x^{2} + 12 t + 2$
2.8.20.3 $x^{8} + 8 x^{7} + 28 x^{6} + 64 x^{5} + 216 x^{4} + 128 x^{3} + 328 x^{2} + 64 x + 124$ $2$ $4$ $2$ $20$ $D_4\times C_2$ (as 8T9) $[3, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(12 t + 12\right) x^{2} + 8 x + 12 t + 10$
2.8.20.5 $x^{8} + 8 x^{7} + 24 x^{6} + 24 x^{5} + 44 x^{4} + 112 x^{3} + 112 x^{2} - 48 x + 36$ $2$ $4$ $2$ $20$ $D_4\times C_2$ (as 8T9) $[3, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(8 t + 8\right) x^{2} + 8 t x + 6$
2.8.20.8 $x^{8} + 12 x^{7} + 78 x^{6} + 308 x^{5} + 795 x^{4} + 1332 x^{3} + 1450 x^{2} + 936 x + 291$ $2$ $4$ $2$ $20$ $D_4\times C_2$ (as 8T9) $[3, 7/2]$ $[2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 12 x^{2} + 8 x + 2$
2.8.22.101 $x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 6$
2.8.22.102 $x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 2$
2.8.22.14 $x^{8} + 4 x^{7} + 18 x^{6} + 56 x^{5} + 131 x^{4} + 200 x^{3} + 234 x^{2} + 316 x + 223$ $2$ $4$ $2$ $22$ $D_4\times C_2$ (as 8T9) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{2} + 8 x + 10$
2.8.22.16 $x^{8} + 8 x^{7} + 72 x^{6} + 48 x^{5} + 108 x^{4} + 176 x^{3} + 176 x^{2} + 224 x + 196$ $2$ $4$ $2$ $22$ $D_4\times C_2$ (as 8T9) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 x + 14$
2.8.22.19 $x^{8} + 16 x^{7} + 60 x^{6} - 40 x^{5} + 96 x^{4} + 544 x^{3} + 40 x^{2} - 144 x + 588$ $2$ $4$ $2$ $22$ $D_4\times C_2$ (as 8T9) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + \left(12 t + 4\right) x^{2} + 8 t x + 4 t + 26$
2.8.22.9 $x^{8} + 20 x^{7} + 138 x^{6} + 432 x^{5} + 979 x^{4} + 1632 x^{3} + 1578 x^{2} + 436 x + 223$ $2$ $4$ $2$ $22$ $D_4\times C_2$ (as 8T9) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 18$
2.8.22.93 $x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{2} + 8 x + 10$
2.8.22.95 $x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 2$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 2$
2.8.22.96 $x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 6$
2.8.22.97 $x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.8.22.98 $x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 14$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 10 x^{4} + 8 x^{3} + 4 x^{2} + 14$
2.8.22.99 $x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 14$ $2$ $8$ $1$ $22$ $D_4\times C_2$ (as 8T9) $[2, 3, 7/2]$ $[2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 4 x^{6} + 6 x^{4} + 12 x^{2} + 14$
2.8.24.17 $x^{8} + 14 x^{4} + 12 x^{2} + 8 x + 6$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 14 x^{4} + 12 x^{2} + 8 x + 6$
2.8.24.21 $x^{8} + 8 x^{7} + 10 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 10 x^{4} + 12 x^{2} + 8 x + 10$
2.8.24.22 $x^{8} + 10 x^{4} + 12 x^{2} + 8 x + 18$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 12 x^{2} + 8 x + 18$
2.8.24.26 $x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 12 x^{2} + 8 x + 14$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 12 x^{2} + 8 x + 14$
2.8.24.27 $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$
2.8.24.37 $x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 6$
2.8.24.38 $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 30$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 12 x^{2} + 8 x + 30$
2.8.24.39 $x^{8} + 8 x^{7} + 14 x^{4} + 12 x^{2} + 8 x + 30$ $2$ $8$ $1$ $24$ $D_4\times C_2$ (as 8T9) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 14 x^{4} + 12 x^{2} + 8 x + 30$
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