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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.22.51 $x^{8} + 16 x^{7} + 64 x^{6} + 24 x^{4} + 192 x^{3} + 156$ $2$ $4$ $2$ $22$ $D_{8}$ (as 8T6) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + 4 t + 14$
2.8.22.52 $x^{8} - 8 x^{7} + 76 x^{6} + 8 x^{5} + 164 x^{4} - 16 x^{3} + 424 x^{2} + 304 x + 724$ $2$ $4$ $2$ $22$ $D_{8}$ (as 8T6) $[3, 4]$ $[2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t + 30$
2.8.24.65 $x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $D_{8}$ (as 8T6) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$
2.8.24.67 $x^{8} + 12 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $8$ $1$ $24$ $D_{8}$ (as 8T6) $[2, 3, 4]$ $[2, 3, 4]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 2$
2.8.27.1 $x^{8} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 18$
2.8.27.115 $x^{8} + 4 x^{6} + 18 x^{4} + 6$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 18 x^{4} + 6$
2.8.27.116 $x^{8} + 4 x^{6} + 2 x^{4} + 6$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 2 x^{4} + 6$
2.8.27.2 $x^{8} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 18$
2.8.27.41 $x^{8} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{5} + 2 x^{4} + 8 x^{2} + 2$
2.8.27.42 $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 18$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 18$
2.8.27.83 $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 6$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 8 x^{2} + 6$
2.8.27.84 $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 6$ $2$ $8$ $1$ $27$ $D_{8}$ (as 8T6) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 10 x^{4} + 8 x^{2} + 6$
2.8.28.101 $x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$
2.8.28.104 $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$
2.8.28.65 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{2} + 10$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{2} + 10$
2.8.28.66 $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 16 x^{2} + 18$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 16 x^{2} + 18$
2.8.28.71 $x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 26$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 26$
2.8.28.72 $x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 24 x^{4} + 24 x^{2} + 2$
2.8.28.97 $x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 10$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 10$
2.8.28.99 $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x + 18$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x + 18$
2.8.31.13 $x^{8} + 18$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 18$
2.8.31.14 $x^{8} + 2$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 2$
2.8.31.15 $x^{8} + 34$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 34$
2.8.31.16 $x^{8} + 50$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 50$
2.8.31.169 $x^{8} + 8 x^{4} + 24 x^{2} + 16 x + 26$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 8 x^{4} + 24 x^{2} + 16 x + 26$
2.8.31.171 $x^{8} + 24 x^{4} + 24 x^{2} + 16 x + 26$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 24 x^{4} + 24 x^{2} + 16 x + 26$
2.8.31.174 $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 34$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 34$
2.8.31.175 $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 50$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 50$
2.8.31.177 $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 2$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 2$
2.8.31.180 $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 18$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 12 x^{4} + 8 x^{2} + 16 x + 18$
2.8.31.233 $x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 18$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 18$
2.8.31.235 $x^{8} + 8 x^{2} + 16 x + 18$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 8 x^{2} + 16 x + 18$
7.8.7.1 $x^{8} + 7$ $7$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 4$ $x^{8} + 7$
7.8.7.2 $x^{8} + 21$ $7$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 4$ $x^{8} + 21$
23.8.7.1 $x^{8} + 23$ $23$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 18$ $x^{8} + 23$
23.8.7.2 $x^{8} + 115$ $23$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 18$ $x^{8} + 115$
31.8.7.1 $x^{8} + 31$ $31$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 28$ $x^{8} + 31$
31.8.7.2 $x^{8} + 93$ $31$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 28$ $x^{8} + 93$
47.8.7.1 $x^{8} + 47$ $47$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 42$ $x^{8} + 47$
47.8.7.2 $x^{8} + 235$ $47$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 42$ $x^{8} + 235$
71.8.7.1 $x^{8} + 71$ $71$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 64$ $x^{8} + 71$
71.8.7.2 $x^{8} + 497$ $71$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 64$ $x^{8} + 497$
79.8.7.1 $x^{8} + 79$ $79$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 76$ $x^{8} + 79$
79.8.7.2 $x^{8} + 237$ $79$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 76$ $x^{8} + 237$
103.8.7.1 $x^{8} + 103$ $103$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 98$ $x^{8} + 103$
103.8.7.2 $x^{8} + 309$ $103$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 98$ $x^{8} + 309$
127.8.7.1 $x^{8} + 127$ $127$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 124$ $x^{8} + 127$
127.8.7.2 $x^{8} + 381$ $127$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 124$ $x^{8} + 381$
151.8.7.1 $x^{8} + 151$ $151$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 145$ $x^{8} + 151$
151.8.7.2 $x^{8} + 453$ $151$ $8$ $1$ $7$ $D_{8}$ (as 8T6) $[\ ]$ $[\ ]_{8}^{2}$ $t + 145$ $x^{8} + 453$
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