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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.18.10 $x^{8} - 4 x^{7} + 26 x^{6} + 8 x^{5} + 132 x^{4} + 72 x^{3} + 252 x^{2} + 80 x + 172$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(6 t + 8\right) x^{2} + 8 t x + 12 t + 14$
2.8.18.11 $x^{8} + 8 x^{7} + 10 x^{6} - 16 x^{5} + 80 x^{4} + 96 x^{3} + 100 x^{2} + 144 x + 84$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 6 t x^{2} + \left(8 t + 8\right) x + 8 t + 10$
2.8.18.12 $x^{8} + 8 x^{7} + 30 x^{6} + 48 x^{5} + 168 x^{4} + 128 x^{3} + 92 x^{2} - 16 x + 4$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(14 t + 14\right) x^{2} + 8 t x + 2$
2.8.18.13 $x^{8} + 8 x^{7} + 14 x^{6} - 16 x^{5} + 8 x^{4} + 128 x^{3} + 124 x^{2} + 48 x + 84$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 2\right) x^{2} + 8 t x + 8 t + 10$
2.8.18.14 $x^{8} + 8 x^{7} + 30 x^{6} + 48 x^{5} + 72 x^{4} + 128 x^{3} + 260 x^{2} - 112 x + 196$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 10\right) x^{2} + 8 t x + 14$
2.8.18.15 $x^{8} - 2 x^{6} - 8 x^{5} + 96 x^{4} + 128 x^{3} + 164 x^{2} + 16 x + 148$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(10 t + 4\right) x^{2} + 8 t x + 8 t + 14$
2.8.18.16 $x^{8} - 14 x^{6} - 8 x^{5} + 216 x^{4} + 224 x^{3} + 92 x^{2} + 16 x + 148$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 14 t x^{2} + 8 t x + 8 t + 14$
2.8.18.9 $x^{8} + 8 x^{7} + 14 x^{6} - 8 x^{5} + 56 x^{4} + 112 x^{3} - 28 x^{2} + 196$ $2$ $4$ $2$ $18$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 2\right) x^{2} + 14$
2.8.22.21 $x^{8} + 16 x^{6} + 8 x^{5} + 112 x^{4} + 64 x^{3} + 448 x^{2} + 240 x + 588$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{2} + \left(8 t + 8\right) x + 4 t + 26$
2.8.22.22 $x^{8} + 16 x^{7} + 88 x^{6} + 184 x^{5} + 96 x^{4} + 32 x^{3} + 256 x^{2} - 16 x + 76$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + 12 x^{2} + 8 t x + 4 t + 10$
2.8.22.23 $x^{8} + 16 x^{7} + 80 x^{6} + 120 x^{5} + 80 x^{4} + 288 x^{3} + 368 x^{2} - 80 x + 268$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + \left(8 t + 12\right) x^{2} + 8 t x + 4 t + 18$
2.8.22.24 $x^{8} - 4 x^{6} + 16 x^{5} + 68 x^{4} - 32 x^{3} + 8 x^{2} + 416 x + 724$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{2} + 8 x + 8 t + 30$
2.8.22.25 $x^{8} - 12 x^{6} + 16 x^{5} + 172 x^{4} - 96 x^{3} + 40 x^{2} + 224 x + 244$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 12 t x^{2} + 8 x + 8 t + 18$
2.8.22.26 $x^{8} + 12 x^{6} + 16 x^{5} + 68 x^{4} + 96 x^{3} + 328 x^{2} + 160 x + 532$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 8\right) x^{2} + 8 x + 24 t + 22$
2.8.22.27 $x^{8} - 4 x^{6} + 16 x^{5} + 28 x^{4} - 32 x^{3} + 88 x^{2} + 96 x + 84$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{2} + 8 x + 8 t + 10$
2.8.22.28 $x^{8} + 20 x^{6} + 16 x^{5} + 92 x^{4} + 160 x^{3} + 8 x^{2} - 160 x + 532$ $2$ $4$ $2$ $22$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 12\right) x^{2} + 8 x + 24 t + 2$
2.8.24.41 $x^{8} + 12 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 12 x^{4} + 8 x^{2} + 8 x + 10$
2.8.24.42 $x^{8} + 12 x^{4} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 12 x^{4} + 8 x + 2$
2.8.24.43 $x^{8} + 12 x^{4} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 12 x^{4} + 8 x + 10$
2.8.24.44 $x^{8} + 4 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 8 x^{2} + 8 x + 10$
2.8.24.45 $x^{8} + 8 x^{4} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{4} + 8 x + 2$
2.8.24.46 $x^{8} + 8 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{2} + 8 x + 2$
2.8.24.47 $x^{8} + 12 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 12 x^{4} + 8 x^{2} + 8 x + 2$
2.8.24.48 $x^{8} + 8 x^{2} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{2} + 8 x + 10$
2.8.24.49 $x^{8} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x + 2$
2.8.24.50 $x^{8} + 8 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{4} + 8 x^{2} + 8 x + 10$
2.8.24.51 $x^{8} + 8 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{4} + 8 x^{2} + 8 x + 2$
2.8.24.52 $x^{8} + 4 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 8 x^{2} + 8 x + 2$
2.8.24.53 $x^{8} + 4 x^{4} + 8 x + 2$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 8 x + 2$
2.8.24.54 $x^{8} + 4 x^{4} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 8 x + 10$
2.8.24.55 $x^{8} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x + 10$
2.8.24.56 $x^{8} + 8 x^{4} + 8 x + 10$ $2$ $8$ $1$ $24$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t + 1$ $x^{8} + 8 x^{4} + 8 x + 10$
2.8.26.33 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 2$
2.8.26.34 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$
2.8.26.35 $x^{8} + 4 x^{6} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{3} + 10$
2.8.26.36 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$
2.8.26.37 $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 10$
2.8.26.38 $x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$
2.8.26.39 $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 2$
2.8.26.40 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 10$
2.8.26.41 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$
2.8.26.42 $x^{8} + 4 x^{6} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{3} + 2$
2.8.26.43 $x^{8} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$
2.8.26.44 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 10$
2.8.26.45 $x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 10$
2.8.26.46 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 10$
2.8.26.47 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 2$
2.8.26.48 $x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 7/2, 4]$ $[2, 2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$
2.8.26.81 $x^{8} + 10 x^{4} + 8 x^{3} + 16 x + 6$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2, 17/4]$ $[2, 3, 7/2, 4, 17/4]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 8 x^{3} + 16 x + 6$
2.8.26.82 $x^{8} + 2 x^{4} + 8 x^{3} + 6$ $2$ $8$ $1$ $26$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 7/2, 17/4]$ $[2, 3, 7/2, 4, 17/4]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 8 x^{3} + 6$
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