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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.8.2 $x^{8} + 8 x^{7} + 56 x^{6} + 240 x^{5} + 816 x^{4} + 2048 x^{3} + 3776 x^{2} + 4928 x + 3760$ $2$ $2$ $4$ $8$ $C_2^2:C_4$ (as 8T10) $[2]$ $[2, 2]^{4}$ $t^{4} + t + 1$ $x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 4 t^{3} + 4 t^{2} + 6$
2.8.12.15 $x^{8} + 4 x^{7} + 4 x^{6} + 12$ $2$ $4$ $2$ $12$ $C_2^2:C_4$ (as 8T10) $[2, 2]$ $[2, 2]^{4}$ $t^{2} + t + 1$ $x^{4} + 2 x^{3} + 4 t + 2$
2.8.12.3 $x^{8} - 12 x^{7} + 44 x^{6} + 152 x^{5} - 512 x^{4} + 560 x^{3} + 4432 x^{2} + 9376 x + 21744$ $2$ $2$ $4$ $12$ $C_2^2:C_4$ (as 8T10) $[3]$ $[2, 3]^{4}$ $t^{4} + t + 1$ $x^{2} + 4 t^{3} x + 4 t^{3} + 12 t + 2$
2.8.16.12 $x^{8} + 8 x^{7} + 14 x^{6} - 12 x^{5} + 12 x^{4} + 40 x^{3} + 124 x^{2} + 72 x + 108$ $2$ $4$ $2$ $16$ $C_2^2:C_4$ (as 8T10) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 2\right) x^{2} + 4 t x + 12 t + 6$
2.8.16.14 $x^{8} + 10 x^{6} - 4 x^{5} + 40 x^{4} - 8 x^{3} + 100 x^{2} + 24 x + 84$ $2$ $4$ $2$ $16$ $C_2^2:C_4$ (as 8T10) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(2 t + 6\right) x^{2} + 4 t x + 8 t + 10$
2.8.16.15 $x^{8} + 8 x^{7} + 18 x^{6} + 12 x^{5} + 52 x^{4} + 72 x^{3} + 60 x^{2} + 40 x + 28$ $2$ $4$ $2$ $16$ $C_2^2:C_4$ (as 8T10) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 4\right) x^{2} + \left(4 t + 4\right) x + 4 t + 6$
2.8.16.17 $x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{5} + 12 x^{4} + 104 x^{3} + 52 x^{2} - 24 x + 156$ $2$ $4$ $2$ $16$ $C_2^2:C_4$ (as 8T10) $[2, 3]$ $[2, 2, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 4 t + 14$
2.8.16.7 $x^{8} + 8 x^{5} + 12 x^{4} + 40 x^{2} + 12$ $2$ $4$ $2$ $16$ $C_2^2:C_4$ (as 8T10) $[2, 3]$ $[2, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 2\right) x^{2} + 4 x + 4 t + 2$
2.8.26.1 $x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$
2.8.26.10 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$
2.8.26.11 $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$
2.8.26.12 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 26$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 26$
2.8.26.13 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$
2.8.26.14 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$
2.8.26.15 $x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 18$
2.8.26.16 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 10$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 10$
2.8.26.2 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 18$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 18$
2.8.26.3 $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$
2.8.26.4 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 2$
2.8.26.5 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 18$
2.8.26.6 $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 10$
2.8.26.7 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 8 x^{3} + 26$
2.8.26.8 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 2$
2.8.26.9 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 26$ $2$ $8$ $1$ $26$ $C_2^2:C_4$ (as 8T10) $[3, 7/2, 4]$ $[2, 3, 7/2, 4]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 26$
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