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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.18.33 $x^{8} + 4 x^{7} + 18 x^{6} + 16 x^{5} + 40 x^{3} + 20 x^{2} + 52$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 2\right) x^{2} + 8 t + 2$
2.8.18.34 $x^{8} + 4 x^{7} + 10 x^{6} + 48 x^{5} + 80 x^{4} + 40 x^{3} + 132 x^{2} + 52$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(10 t + 2\right) x^{2} + 8 t + 2$
2.8.18.35 $x^{8} + 6 x^{6} + 8 x^{5} + 36 x^{4} + 96 x^{3} + 100 x^{2} + 48 x + 12$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(6 t + 6\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$
2.8.18.36 $x^{8} - 2 x^{6} + 8 x^{5} + 148 x^{4} + 160 x^{3} + 148 x^{2} + 48 x + 12$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(14 t + 6\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$
2.8.18.45 $x^{8} + 8 x^{7} + 18 x^{6} + 4 x^{4} + 96 x^{3} + 180 x^{2} + 112 x + 124$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 4\right) x^{2} + 8 t x + 12 t + 10$
2.8.18.46 $x^{8} + 14 x^{6} + 8 x^{5} + 84 x^{4} + 128 x^{3} + 156 x^{2} + 80 x + 28$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(6 t + 10\right) x^{2} + \left(8 t + 8\right) x + 4 t + 6$
2.8.18.47 $x^{8} + 8 x^{7} + 30 x^{6} + 72 x^{5} + 284 x^{4} + 208 x^{3} + 316 x^{2} + 192 x + 156$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(14 t + 14\right) x^{2} + 8 x + 4 t + 14$
2.8.18.48 $x^{8} + 14 x^{6} + 16 x^{5} + 84 x^{4} + 112 x^{3} + 156 x^{2} + 64 x + 28$ $2$ $4$ $2$ $18$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(6 t + 10\right) x^{2} + 8 x + 4 t + 6$
2.8.20.21 $x^{8} + 4 x^{7} + 40 x^{6} + 40 x^{5} + 196 x^{4} - 56 x^{3} + 304 x^{2} - 80 x + 100$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 12 x^{2} + 8 t x + 10$
2.8.20.26 $x^{8} - 4 x^{7} + 32 x^{6} + 32 x^{5} + 100 x^{4} + 88 x^{3} + 224 x^{2} + 160 x + 100$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(8 t + 12\right) x^{2} + 8 x + 10$
2.8.20.27 $x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 120 x^{4} + 88 x^{3} + 232 x^{2} + 124$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 12 t + 10$
2.8.20.31 $x^{8} + 4 x^{7} + 24 x^{6} + 16 x^{5} + 36 x^{4} + 40 x^{3} + 80 x^{2} + 100$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + 4 x^{2} + 10$
2.8.20.37 $x^{8} + 4 x^{7} + 28 x^{6} + 96 x^{5} + 136 x^{4} + 56 x^{3} + 168 x^{2} + 124$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 12\right) x^{2} + 12 t + 2$
2.8.20.39 $x^{8} + 4 x^{7} + 36 x^{6} + 72 x^{5} + 184 x^{4} + 216 x^{3} + 216 x^{2} + 176 x + 124$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 12\right) x^{2} + \left(8 t + 8\right) x + 12 t + 10$
2.8.20.42 $x^{8} + 4 x^{7} + 12 x^{6} + 64 x^{5} + 104 x^{4} + 56 x^{3} + 232 x^{2} + 124$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + 12 t + 2$
2.8.20.47 $x^{8} - 4 x^{7} + 36 x^{6} - 16 x^{5} + 128 x^{4} - 8 x^{3} + 184 x^{2} + 76$ $2$ $4$ $2$ $20$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2]$ $[2, 2, 3, 7/2, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 t x^{3} + \left(4 t + 12\right) x^{2} + 4 t + 10$
2.8.27.100 $x^{8} + 8 x^{7} + 26 x^{4} + 8 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 26 x^{4} + 8 x^{2} + 22$
2.8.27.101 $x^{8} + 8 x^{7} + 8 x^{6} + 26 x^{4} + 24 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 26 x^{4} + 24 x^{2} + 6$
2.8.27.102 $x^{8} + 8 x^{7} + 8 x^{6} + 18 x^{4} + 8 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 18 x^{4} + 8 x^{2} + 6$
2.8.27.103 $x^{8} + 8 x^{7} + 26 x^{4} + 24 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 26 x^{4} + 24 x^{2} + 22$
2.8.27.104 $x^{8} + 8 x^{7} + 8 x^{6} + 26 x^{4} + 8 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 26 x^{4} + 8 x^{2} + 6$
2.8.27.129 $x^{8} + 8 x^{6} + 10 x^{4} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 10 x^{4} + 22$
2.8.27.130 $x^{8} + 10 x^{4} + 16 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 16 x^{2} + 6$
2.8.27.131 $x^{8} + 2 x^{4} + 16 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 16 x^{2} + 6$
2.8.27.132 $x^{8} + 8 x^{6} + 2 x^{4} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 2 x^{4} + 22$
2.8.27.133 $x^{8} + 8 x^{6} + 2 x^{4} + 16 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 2 x^{4} + 16 x^{2} + 22$
2.8.27.134 $x^{8} + 2 x^{4} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 2 x^{4} + 6$
2.8.27.135 $x^{8} + 10 x^{4} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 10 x^{4} + 6$
2.8.27.136 $x^{8} + 8 x^{6} + 10 x^{4} + 16 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 10 x^{4} + 16 x^{2} + 22$
2.8.27.97 $x^{8} + 8 x^{7} + 2 x^{4} + 8 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 2 x^{4} + 8 x^{2} + 22$
2.8.27.98 $x^{8} + 8 x^{7} + 8 x^{6} + 18 x^{4} + 24 x^{2} + 6$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 18 x^{4} + 24 x^{2} + 6$
2.8.27.99 $x^{8} + 8 x^{7} + 2 x^{4} + 24 x^{2} + 22$ $2$ $8$ $1$ $27$ $(C_4^2 : C_2):C_2$ (as 8T26) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 4, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 2 x^{4} + 24 x^{2} + 22$
2.8.28.113 $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 2$
2.8.28.114 $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 10$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 10$
2.8.28.115 $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x^{2} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x^{2} + 2$
2.8.28.116 $x^{8} + 12 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 26$
2.8.28.117 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 18$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 18$
2.8.28.118 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 2$
2.8.28.119 $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{2} + 10$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{2} + 10$
2.8.28.120 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{3} + 26$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{3} + 26$
2.8.28.121 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$
2.8.28.122 $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$
2.8.28.123 $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 2$
2.8.28.124 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 18$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 18$
2.8.28.125 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 10$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 10$
2.8.28.126 $x^{8} + 12 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 2$
2.8.28.127 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$
2.8.28.128 $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 26$
2.8.28.81 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 18$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 18$
2.8.28.82 $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 16 x + 10$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (as 8T26) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 16 x + 10$
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