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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.31.1 $x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 50$ $2$ $8$ $1$ $31$ $C_8$ (as 8T1) $[3, 4, 5]$ $[3, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 50$
2.8.31.10 $x^{8} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 34$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 34$
2.8.31.100 $x^{8} + 24 x^{6} + 16 x^{3} + 26$ $2$ $8$ $1$ $31$ $QD_{16}$ (as 8T8) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 24 x^{6} + 16 x^{3} + 26$
2.8.31.101 $x^{8} + 16 x^{6} + 4 x^{4} + 16 x^{3} + 58$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{6} + 4 x^{4} + 16 x^{3} + 58$
2.8.31.102 $x^{8} + 8 x^{6} + 4 x^{4} + 26$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 26$
2.8.31.103 $x^{8} + 4 x^{4} + 16 x^{3} + 42$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 16 x^{3} + 42$
2.8.31.104 $x^{8} + 20 x^{4} + 16 x^{3} + 10$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 20 x^{4} + 16 x^{3} + 10$
2.8.31.105 $x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 26$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 26$
2.8.31.106 $x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 10$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 10$
2.8.31.107 $x^{8} + 8 x^{6} + 4 x^{4} + 10$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 10$
2.8.31.108 $x^{8} + 8 x^{6} + 4 x^{4} + 58$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 58$
2.8.31.109 $x^{8} + 10$ $2$ $8$ $1$ $31$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4, 5]$ $[2, 3, 4, 5]^{2}$ $t + 1$ $x^{8} + 10$
2.8.31.11 $x^{8} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 18$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 4 x^{4} + 16 x^{3} + 16 x^{2} + 18$
2.8.31.110 $x^{8} + 26$ $2$ $8$ $1$ $31$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4, 5]$ $[2, 3, 4, 5]^{2}$ $t + 1$ $x^{8} + 26$
2.8.31.111 $x^{8} + 42$ $2$ $8$ $1$ $31$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4, 5]$ $[2, 3, 4, 5]^{2}$ $t + 1$ $x^{8} + 42$
2.8.31.112 $x^{8} + 58$ $2$ $8$ $1$ $31$ $Z_8 : Z_8^\times$ (as 8T15) $[3, 4, 5]$ $[2, 3, 4, 5]^{2}$ $t + 1$ $x^{8} + 58$
2.8.31.113 $x^{8} + 4 x^{4} + 42$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 42$
2.8.31.114 $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 58$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 58$
2.8.31.115 $x^{8} + 4 x^{4} + 58$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 58$
2.8.31.116 $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 10$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 10$
2.8.31.117 $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 42$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 42$
2.8.31.118 $x^{8} + 4 x^{4} + 10$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 10$
2.8.31.119 $x^{8} + 4 x^{4} + 26$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 26$
2.8.31.12 $x^{8} + 20 x^{4} + 16 x^{3} + 16 x^{2} + 34$ $2$ $8$ $1$ $31$ $C_8:C_2$ (as 8T7) $[3, 4, 5]$ $[3, 4, 5]^{2}$ $t + 1$ $x^{8} + 20 x^{4} + 16 x^{3} + 16 x^{2} + 34$
2.8.31.120 $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 26$ $2$ $8$ $1$ $31$ $(C_8:C_2):C_2$ (as 8T16) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 26$
2.8.31.121 $x^{8} + 16 x^{7} + 8 x^{6} + 10$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 8 x^{6} + 10$
2.8.31.122 $x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 58$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 58$
2.8.31.123 $x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 58$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 58$
2.8.31.124 $x^{8} + 8 x^{6} + 26$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 26$
2.8.31.125 $x^{8} + 16 x^{3} + 58$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{3} + 58$
2.8.31.126 $x^{8} + 16 x^{5} + 16 x^{3} + 26$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{5} + 16 x^{3} + 26$
2.8.31.127 $x^{8} + 16 x^{5} + 24 x^{4} + 16 x^{3} + 42$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{5} + 24 x^{4} + 16 x^{3} + 42$
2.8.31.128 $x^{8} + 8 x^{6} + 58$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 58$
2.8.31.129 $x^{8} + 16 x^{5} + 24 x^{4} + 16 x^{3} + 58$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{5} + 24 x^{4} + 16 x^{3} + 58$
2.8.31.13 $x^{8} + 18$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 18$
2.8.31.130 $x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 42$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{6} + 16 x^{5} + 16 x^{3} + 42$
2.8.31.131 $x^{8} + 8 x^{6} + 10$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 10$
2.8.31.132 $x^{8} + 16 x^{7} + 8 x^{6} + 42$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 8 x^{6} + 42$
2.8.31.133 $x^{8} + 8 x^{6} + 42$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 42$
2.8.31.134 $x^{8} + 24 x^{6} + 16 x^{5} + 42$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 24 x^{6} + 16 x^{5} + 42$
2.8.31.135 $x^{8} + 8 x^{6} + 16 x^{5} + 10$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 8 x^{6} + 16 x^{5} + 10$
2.8.31.136 $x^{8} + 16 x^{3} + 26$ $2$ $8$ $1$ $31$ $C_4\wr C_2$ (as 8T17) $[3, 4, 5]$ $[2, 3, 7/2, 4, 5]$ $t + 1$ $x^{8} + 16 x^{3} + 26$
2.8.31.137 $x^{8} + 28 x^{4} + 8 x^{2} + 10$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 28 x^{4} + 8 x^{2} + 10$
2.8.31.138 $x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 42$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 42$
2.8.31.139 $x^{8} + 28 x^{4} + 8 x^{2} + 58$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 28 x^{4} + 8 x^{2} + 58$
2.8.31.14 $x^{8} + 2$ $2$ $8$ $1$ $31$ $D_{8}$ (as 8T6) $[3, 4, 5]$ $[2, 3, 4, 5]$ $t + 1$ $x^{8} + 2$
2.8.31.140 $x^{8} + 4 x^{4} + 8 x^{2} + 10$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 4 x^{4} + 8 x^{2} + 10$
2.8.31.141 $x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 26$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 26$
2.8.31.142 $x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 26$
2.8.31.143 $x^{8} + 16 x^{5} + 20 x^{4} + 24 x^{2} + 26$ $2$ $8$ $1$ $31$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[3, 4, 5]$ $[2, 3, 7/2, 4, 17/4, 5]$ $t + 1$ $x^{8} + 16 x^{5} + 20 x^{4} + 24 x^{2} + 26$
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