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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.16.41 $x^{8} - 2 x^{6} + 8 x^{5} + 32 x^{4} - 8 x^{3} + 12 x^{2} + 16 x + 4$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(6 t + 2\right) x^{2} + 4 x + 2$
2.8.16.42 $x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 16 x^{3} + 28 x^{2} + 24 x + 12$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t + 2$
2.8.16.43 $x^{8} + 8 x^{7} + 18 x^{6} + 12 x^{5} + 32 x^{4} + 64 x^{3} + 52 x^{2} + 72 x + 84$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 8 t + 10$
2.8.16.44 $x^{8} + 8 x^{7} + 22 x^{6} + 32 x^{5} + 52 x^{4} + 56 x^{3} + 52 x^{2} + 32 x + 28$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t + 4\right) x^{2} + 4 x + 4 t + 6$
2.8.16.49 $x^{8} + 8 x^{7} + 18 x^{6} + 16 x^{5} + 68 x^{4} + 40 x^{3} + 132 x^{2} + 32 x + 124$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 4\right) x^{2} + 4 x + 12 t + 10$
2.8.16.50 $x^{8} + 8 x^{7} + 22 x^{6} + 28 x^{5} + 80 x^{4} + 160 x^{3} + 100 x^{2} + 56 x + 196$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t + 4\right) x + 14$
2.8.16.51 $x^{8} + 6 x^{6} + 8 x^{5} + 12 x^{4} + 24 x^{3} + 28 x^{2} + 12$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(2 t + 4\right) x^{2} + 4 x + 4 t + 2$
2.8.16.52 $x^{8} + 6 x^{6} + 4 x^{5} + 60 x^{4} + 48 x^{3} + 124 x^{2} + 72 x + 156$ $2$ $4$ $2$ $16$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3]$ $[2, 2, 3, 3]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(6 t + 6\right) x^{2} + \left(4 t + 4\right) x + 4 t + 14$
2.8.20.93 $x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 2$ $2$ $8$ $1$ $20$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 2$
2.8.20.94 $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 14$ $2$ $8$ $1$ $20$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 14$
2.8.20.95 $x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 14$ $2$ $8$ $1$ $20$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 14$
2.8.20.96 $x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x + 10$ $2$ $8$ $1$ $20$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 2, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t + 1$ $x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x + 10$
2.8.22.67 $x^{8} + 12 x^{6} + 8 x^{5} + 76 x^{4} + 96 x^{3} + 328 x^{2} + 304 x + 388$ $2$ $4$ $2$ $22$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4]$ $[2, 2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 16 t + 22$
2.8.22.68 $x^{8} + 12 x^{6} + 8 x^{5} + 60 x^{4} + 96 x^{3} + 232 x^{2} + 240 x + 228$ $2$ $4$ $2$ $22$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4]$ $[2, 2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 16 t + 14$
2.8.22.69 $x^{8} + 16 x^{7} + 64 x^{6} + 32 x^{4} + 256 x^{3} + 844$ $2$ $4$ $2$ $22$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4]$ $[2, 2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + 28 t + 30$
2.8.22.70 $x^{8} + 16 x^{7} + 52 x^{6} - 88 x^{5} + 220 x^{4} + 192 x^{3} - 8 x^{2} + 48 x + 36$ $2$ $4$ $2$ $22$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4]$ $[2, 2, 3, 4]^{2}$ $t^{2} + t + 1$ $x^{4} + 8 x^{3} + 12 t x^{2} + \left(8 t + 8\right) x + 6$
2.8.24.77 $x^{8} + 8 x^{7} + 8 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$ $2$ $8$ $1$ $24$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$
2.8.24.78 $x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 26$ $2$ $8$ $1$ $24$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 26$
2.8.24.79 $x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 26$ $2$ $8$ $1$ $24$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 14 x^{4} + 4 x^{2} + 8 x + 26$
2.8.24.80 $x^{8} + 8 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$ $2$ $8$ $1$ $24$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 14$
2.8.27.117 $x^{8} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 22$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 22$
2.8.27.118 $x^{8} + 4 x^{6} + 2 x^{4} + 16 x + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 2 x^{4} + 16 x + 6$
2.8.27.119 $x^{8} + 8 x^{5} + 2 x^{4} + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{5} + 2 x^{4} + 6$
2.8.27.120 $x^{8} + 4 x^{6} + 26 x^{4} + 16 x^{3} + 16 x + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 26 x^{4} + 16 x^{3} + 16 x + 6$
2.8.27.45 $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 16 x^{2} + 2$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 16 x^{2} + 2$
2.8.27.46 $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 16 x^{2} + 16 x + 2$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 16 x^{2} + 16 x + 2$
2.8.27.47 $x^{8} + 8 x^{7} + 8 x^{5} + 18 x^{4} + 16 x^{2} + 26$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 18 x^{4} + 16 x^{2} + 26$
2.8.27.48 $x^{8} + 8 x^{7} + 8 x^{5} + 10 x^{4} + 10$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 10 x^{4} + 10$
2.8.27.5 $x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 2$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 2$
2.8.27.6 $x^{8} + 8 x^{5} + 10 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{5} + 10 x^{4} + 8 x^{2} + 26$
2.8.27.7 $x^{8} + 4 x^{6} + 18 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 18 x^{4} + 8 x^{2} + 18$
2.8.27.8 $x^{8} + 8 x^{5} + 10 x^{4} + 16 x^{3} + 24 x^{2} + 26$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{5} + 10 x^{4} + 16 x^{3} + 24 x^{2} + 26$
2.8.27.85 $x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 24 x^{2} + 16 x + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 24 x^{2} + 16 x + 6$
2.8.27.86 $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 8 x^{2} + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 2 x^{4} + 8 x^{2} + 6$
2.8.27.87 $x^{8} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 30$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 26 x^{4} + 30$
2.8.27.88 $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 24 x^{2} + 6$ $2$ $8$ $1$ $27$ $Z_8 : Z_8^\times$ (as 8T15) $[2, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 26 x^{4} + 24 x^{2} + 6$
2.8.28.105 $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 2$
2.8.28.106 $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x + 10$
2.8.28.107 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{2} + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{2} + 2$
2.8.28.108 $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 26$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 26$
2.8.28.109 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{3} + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{3} + 10$
2.8.28.110 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 2$
2.8.28.111 $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 16 x + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 16 x^{2} + 16 x + 2$
2.8.28.112 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 10$
2.8.28.73 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{2} + 10$
2.8.28.74 $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 24 x^{2} + 18$
2.8.28.75 $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{4} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{4} + 24 x^{2} + 10$
2.8.28.76 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{2} + 2$
2.8.28.77 $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{3} + 24 x^{2} + 10$
2.8.28.78 $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 16 x^{4} + 24 x^{2} + 18$
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