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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.12.20 $x^{8} - 2 x^{7} + 2 x^{6} + 8 x^{5} + 8 x^{4} - 4 x^{3} - 4 x^{2} + 4$ $2$ $4$ $2$ $12$ $C_2^3: C_4$ (as 8T21) $[2, 2]$ $[2, 2, 2]^{4}$ $t^{2} + t + 1$ $x^{4} + 2 t x^{3} + 2 t x^{2} + 2$
2.8.16.30 $x^{8} - 4 x^{7} + 28 x^{6} - 16 x^{5} + 24 x^{4} + 88 x^{3} + 40 x^{2} + 16 x + 52$ $2$ $4$ $2$ $16$ $C_2^3: C_4$ (as 8T21) $[2, 3]$ $[2, 2, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 8 t + 6$
2.8.16.39 $x^{8} + 4 x^{6} - 4 x^{5} + 32 x^{4} - 8 x^{3} + 72 x^{2} - 56 x + 196$ $2$ $4$ $2$ $16$ $C_2^3: C_4$ (as 8T21) $[2, 3]$ $[2, 3, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + 2 x^{2} + 4 t x + 14$
2.8.16.40 $x^{8} + 8 x^{6} - 4 x^{5} + 56 x^{4} + 8 x^{3} + 128 x^{2} - 56 x + 196$ $2$ $4$ $2$ $16$ $C_2^3: C_4$ (as 8T21) $[2, 3]$ $[2, 3, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 6\right) x^{2} + 4 t x + 14$
2.8.18.17 $x^{8} + 8 x^{7} + 28 x^{6} + 48 x^{5} + 56 x^{4} + 80 x^{3} + 120 x^{2} + 148$ $2$ $4$ $2$ $18$ $C_2^3: C_4$ (as 8T21) $[2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 6 x^{2} + 8 t + 14$
2.8.18.18 $x^{8} + 28 x^{6} + 8 x^{5} + 224 x^{4} + 112 x^{3} + 456 x^{2} + 112 x + 196$ $2$ $4$ $2$ $18$ $C_2^3: C_4$ (as 8T21) $[2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 14 x^{2} + \left(8 t + 8\right) x + 14$
2.8.18.19 $x^{8} + 4 x^{7} + 36 x^{6} + 88 x^{5} + 168 x^{4} + 88 x^{3} + 296 x^{2} + 148$ $2$ $4$ $2$ $18$ $C_2^3: C_4$ (as 8T21) $[2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t + 14\right) x^{2} + 8 t + 14$
2.8.18.20 $x^{8} + 8 x^{6} + 16 x^{5} + 40 x^{4} + 64 x^{3} + 160 x^{2} + 96 x + 84$ $2$ $4$ $2$ $18$ $C_2^3: C_4$ (as 8T21) $[2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 6\right) x^{2} + 8 x + 8 t + 10$
2.8.25.1 $x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 16 x + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 16 x + 2$
2.8.25.2 $x^{8} + 8 x^{7} + 12 x^{6} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 14 x^{4} + 8 x^{3} + 28 x^{2} + 2$
2.8.25.3 $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 2$
2.8.25.33 $x^{8} + 2 x^{4} + 20 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 20 x^{2} + 10$
2.8.25.34 $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 10$
2.8.25.35 $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 10$
2.8.25.36 $x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 28 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 28 x^{2} + 10$
2.8.25.37 $x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 4 x^{6} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.8.25.38 $x^{8} + 2 x^{4} + 4 x^{2} + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 4 x^{2} + 10$
2.8.25.39 $x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 2 x^{4} + 4 x^{2} + 16 x + 10$
2.8.25.4 $x^{8} + 2 x^{4} + 20 x^{2} + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 20 x^{2} + 2$
2.8.25.40 $x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 10$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 10$
2.8.25.5 $x^{8} + 2 x^{4} + 4 x^{2} + 16 x + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 4 x^{2} + 16 x + 2$
2.8.25.6 $x^{8} + 2 x^{4} + 4 x^{2} + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 4 x^{2} + 2$
2.8.25.7 $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 2 x^{4} + 20 x^{2} + 2$
2.8.25.8 $x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 2$ $2$ $8$ $1$ $25$ $C_2^3: C_4$ (as 8T21) $[2, 3, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 2 x^{4} + 20 x^{2} + 16 x + 2$
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