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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.30.1 $x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 18$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 18$
2.8.30.10 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 10$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 10$
2.8.30.100 $x^{8} + 8 x^{7} + 8 x^{6} + 24 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 24 x^{2} + 10$
2.8.30.101 $x^{8} + 8 x^{7} + 16 x^{6} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 10$
2.8.30.102 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x^{2} + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x^{2} + 18$
2.8.30.103 $x^{8} + 8 x^{7} + 16 x^{3} + 16 x + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{3} + 16 x + 18$
2.8.30.104 $x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 16 x + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 16 x + 18$
2.8.30.105 $x^{8} + 8 x^{7} + 16 x^{5} + 8 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 8 x^{2} + 10$
2.8.30.106 $x^{8} + 8 x^{7} + 24 x^{2} + 16 x + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{2} + 16 x + 18$
2.8.30.107 $x^{8} + 8 x^{7} + 16 x^{6} + 24 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 24 x^{2} + 10$
2.8.30.108 $x^{8} + 8 x^{7} + 24 x^{4} + 24 x^{2} + 16 x + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{4} + 24 x^{2} + 16 x + 18$
2.8.30.109 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{4} + 8 x^{2} + 2$
2.8.30.11 $x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 26$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 20 x^{4} + 26$
2.8.30.110 $x^{8} + 8 x^{7} + 16 x^{3} + 8 x^{2} + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{3} + 8 x^{2} + 18$
2.8.30.111 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 8 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 8 x^{2} + 10$
2.8.30.112 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 2$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 2$
2.8.30.113 $x^{8} + 8 x^{7} + 16 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{4} + 8 x^{2} + 18$
2.8.30.114 $x^{8} + 8 x^{7} + 16 x^{5} + 8 x^{2} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 8 x^{2} + 26$
2.8.30.115 $x^{8} + 8 x^{7} + 16 x^{5} + 16 x + 2$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 16 x + 2$
2.8.30.116 $x^{8} + 8 x^{7} + 16 x^{5} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 10$
2.8.30.117 $x^{8} + 8 x^{7} + 8 x^{2} + 2$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{2} + 2$
2.8.30.118 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 8 x^{2} + 16 x + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 8 x^{2} + 16 x + 10$
2.8.30.119 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{3} + 24 x^{2} + 16 x + 2$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{3} + 24 x^{2} + 16 x + 2$
2.8.30.12 $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 26$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 26$
2.8.30.120 $x^{8} + 8 x^{7} + 8 x^{6} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 26$
2.8.30.121 $x^{8} + 8 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$
2.8.30.122 $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 24 x^{2} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 24 x^{2} + 26$
2.8.30.123 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x^{2} + 10$
2.8.30.124 $x^{8} + 8 x^{7} + 16 x + 18$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x + 18$
2.8.30.125 $x^{8} + 8 x^{7} + 16 x^{5} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 26$
2.8.30.126 $x^{8} + 8 x^{7} + 8 x^{2} + 10$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{2} + 10$
2.8.30.127 $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 26$
2.8.30.128 $x^{8} + 8 x^{7} + 26$ $2$ $8$ $1$ $30$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 26$
2.8.30.13 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 12 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 12 x^{4} + 24 x^{2} + 2$
2.8.30.14 $x^{8} + 8 x^{7} + 16 x^{5} + 20 x^{4} + 26$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{5} + 20 x^{4} + 26$
2.8.30.15 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 2$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 2$
2.8.30.16 $x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$
2.8.30.17 $x^{8} + 8 x^{7} + 24 x^{6} + 12 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 12 x^{4} + 24 x^{2} + 18$
2.8.30.18 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 2$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 2$
2.8.30.19 $x^{8} + 8 x^{7} + 8 x^{6} + 28 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 28 x^{4} + 24 x^{2} + 2$
2.8.30.2 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 12 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 12 x^{4} + 24 x^{2} + 18$
2.8.30.20 $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 26$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 20 x^{4} + 26$
2.8.30.21 $x^{8} + 8 x^{7} + 16 x^{6} + 12 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 16 x^{6} + 12 x^{4} + 8 x^{2} + 18$
2.8.30.22 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 24 x^{2} + 2$
2.8.30.23 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 28 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 28 x^{4} + 24 x^{2} + 18$
2.8.30.24 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 12 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $30$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 12 x^{4} + 8 x^{2} + 18$
2.8.30.25 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 16 x^{2} + 10$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 16 x^{2} + 10$
2.8.30.26 $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 26$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 20 x^{4} + 26$
2.8.30.27 $x^{8} + 8 x^{7} + 20 x^{4} + 10$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 20 x^{4} + 10$
2.8.30.28 $x^{8} + 8 x^{7} + 24 x^{6} + 20 x^{4} + 18$ $2$ $8$ $1$ $30$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[3, 4, 19/4]$ $[2, 3, 7/2, 4, 17/4, 19/4]$ $t + 1$ $x^{8} + 8 x^{7} + 24 x^{6} + 20 x^{4} + 18$
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