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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.28.1 $x^{8} + 8 x^{5} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 24 x^{2} + 18$
2.8.28.10 $x^{8} + 8 x^{5} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 8 x^{2} + 26$
2.8.28.100 $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $QD_{16}$ (as 8T8) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 2$
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) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 26$
2.8.28.102 $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x^{2} + 26$ $2$ $8$ $1$ $28$ $QD_{16}$ (as 8T8) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 16 x^{2} + 26$
2.8.28.103 $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $QD_{16}$ (as 8T8) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 20 x^{4} + 8 x^{2} + 10$
2.8.28.104 $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$ $2$ $8$ $1$ $28$ $D_{8}$ (as 8T6) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 12 x^{4} + 2$
2.8.28.105 $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 2$ $2$ $8$ $1$ $28$ $Z_8 : Z_8^\times$ (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) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{3} + 10$
2.8.28.11 $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 18$
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) $[3, 7/2, 9/2]$ $[2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 16 x^{2} + 10$
2.8.28.113 $x^{8} + 4 x^{6} + 8 x^{5} + 28 x^{4} + 2$ $2$ $8$ $1$ $28$ $(C_4^2 : C_2):C_2$ (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) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 16 x^{2} + 10$
2.8.28.12 $x^{8} + 8 x^{5} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 24 x^{2} + 2$
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) $[3, 7/2, 9/2]$ $[2, 2, 3, 7/2, 9/2]^{2}$ $t + 1$ $x^{8} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{2} + 26$
2.8.28.13 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$
2.8.28.14 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$
2.8.28.15 $x^{8} + 8 x^{5} + 24 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 24 x^{2} + 26$
2.8.28.16 $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 26$
2.8.28.17 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$
2.8.28.18 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$
2.8.28.19 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$
2.8.28.2 $x^{8} + 8 x^{6} + 8 x^{5} + 8 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 8 x^{2} + 18$
2.8.28.20 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$
2.8.28.21 $x^{8} + 8 x^{6} + 8 x^{5} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 8 x^{2} + 10$
2.8.28.22 $x^{8} + 8 x^{5} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 24 x^{2} + 10$
2.8.28.23 $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 10$
2.8.28.24 $x^{8} + 8 x^{5} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 8 x^{2} + 10$
2.8.28.25 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$
2.8.28.26 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$
2.8.28.27 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$
2.8.28.28 $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3 : C_4 $ (as 8T19) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{6} + 8 x^{5} + 24 x^{2} + 2$
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