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Label Polynomial $p$ $e$ $f$ $c$ Galois group Slope content
2.8.0.1 x8 + x4 + x3 + x + 1 2 1 8 0 $C_8$ (as 8T1) $ [\ ]^{8}$
2.8.8.1 x8 + 28x4 + 144 2 2 4 8 $C_4\times C_2$ (as 8T2) $ [2]^{4}$
2.8.8.10 x8 + 2x6 + 8x3 + 16 2 2 4 8 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 2]^{4}$
2.8.8.11 x8 + 20x2 + 4 2 4 2 8 $S_4$ (as 8T14) $ [4/3, 4/3]_{3}^{2}$
2.8.8.12 x8 + 2x5 + 2x4 + 4 2 4 2 8 $A_4\wr C_2$ (as 8T42) $ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.8.8.13 x8 + 2x + 2 2 8 1 8 $C_2^3:(C_7: C_3)$ (as 8T36) $ [8/7, 8/7, 8/7]_{7}^{3}$
2.8.8.2 x8 + 2x7 + 8x2 + 48 2 2 4 8 $C_2^2:C_4$ (as 8T10) $ [2, 2]^{4}$
2.8.8.3 x8 + 2x7 + 2x6 + 16 2 2 4 8 $C_2^3: C_4$ (as 8T20) $ [2, 2, 2]^{4}$
2.8.8.4 x8 + 2x7 + 2x6 + 8x3 + 48 2 2 4 8 $C_8$ (as 8T1) $ [2]^{4}$
2.8.8.5 x8 + 2x7 + 8x2 + 16 2 2 4 8 $C_8:C_2$ (as 8T7) $ [2, 2]^{4}$
2.8.8.6 x8 + 2x7 + 2x6 + 16x2 + 16 2 2 4 8 $(C_8:C_2):C_2$ (as 8T16) $ [2, 2, 2]^{4}$
2.8.8.7 x8 + 2x6 + 4x5 + 16 2 2 4 8 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 2]^{4}$
2.8.8.8 x8 + 4x5 + 8x2 + 48 2 2 4 8 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 2]^{4}$
2.8.8.9 x8 + 6x6 + 4x5 + 16 2 2 4 8 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 2]^{4}$
2.8.10.1 x8 + 2x3 + 2 2 8 1 10 $C_2^3:(C_7: C_3)$ (as 8T36) $ [10/7, 10/7, 10/7]_{7}^{3}$
2.8.10.2 x8 + 20x2 + 20 2 8 1 10 $\textrm{GL(2,3)}$ (as 8T23) $ [4/3, 4/3, 3/2]_{3}^{2}$
2.8.10.3 x8 + 4x2 + 20 2 8 1 10 $\textrm{GL(2,3)}$ (as 8T23) $ [4/3, 4/3, 3/2]_{3}^{2}$
2.8.12.1 x8 + 6x6 + 8x5 + 16 2 2 4 12 $C_4\times C_2$ (as 8T2) $ [3]^{4}$
2.8.12.10 x8 + 2x6 + 112 2 2 4 12 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 3]^{4}$
2.8.12.11 x8 + 6x6 + 48 2 2 4 12 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 3]^{4}$
2.8.12.12 x8 + 2x6 + 48 2 2 4 12 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 3]^{4}$
2.8.12.13 x8 + 12x4 + 16 2 4 2 12 $D_4$ (as 8T4) $ [2, 2]^{2}$
2.8.12.14 x8 + 12x4 + 144 2 4 2 12 $D_4$ (as 8T4) $ [2, 2]^{2}$
2.8.12.15 x8 + 2x7 + 2x4 + 12 2 4 2 12 $C_2^2:C_4$ (as 8T10) $ [2, 2]^{4}$
2.8.12.16 x8 + 24x2 + 4 2 4 2 12 $A_4\times C_2$ (as 8T13) $ [2, 2]^{6}$
2.8.12.17 x8 + 2x7 + 2x6 + 2x4 + 4 2 4 2 12 $C_2^4:C_6$ (as 8T33) $ [2, 2, 2, 2]^{6}$
2.8.12.18 x8 + 8x7 + 48 2 4 2 12 $C_2^4:C_6$ (as 8T33) $ [2, 2, 2, 2]^{6}$
2.8.12.19 x8 + 12x4 + 80 2 4 2 12 $(C_8:C_2):C_2$ (as 8T16) $ [2, 2, 2]^{4}$
2.8.12.2 x8 + 2x6 + 8x4 + 16 2 2 4 12 $C_4\times C_2$ (as 8T2) $ [3]^{4}$
2.8.12.20 x8 + 8x6 + 12x4 + 80 2 4 2 12 $C_2^3: C_4$ (as 8T21) $ [2, 2, 2]^{4}$
2.8.12.21 x8 + 12x6 + 12x4 + 80 2 4 2 12 $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $ [2, 2, 2, 2]^{4}$
2.8.12.22 x8 + 4x7 + 16x3 + 48 2 4 2 12 $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $ [2, 2, 2, 2]^{4}$
2.8.12.23 x8 + 8x5 + 4x4 + 48 2 4 2 12 $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $ [2, 2, 2, 2]^{4}$
2.8.12.24 x8 + 4x6 + 28x4 + 80 2 4 2 12 $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $ [2, 2, 2, 2]^{4}$
2.8.12.25 x8 + 28x2 + 4 2 8 1 12 $S_4\times C_2$ (as 8T24) $ [4/3, 4/3, 2]_{3}^{2}$
2.8.12.26 x8 + 12x2 + 4 2 8 1 12 $S_4\times C_2$ (as 8T24) $ [4/3, 4/3, 2]_{3}^{2}$
2.8.12.27 x8 + 4x5 + 4 2 8 1 12 $C_2^3:(C_7: C_3)$ (as 8T36) $ [12/7, 12/7, 12/7]_{7}^{3}$
2.8.12.28 x8 + 2x5 + 2 2 8 1 12 $C_2^3:(C_7: C_3)$ (as 8T36) $ [12/7, 12/7, 12/7]_{7}^{3}$
2.8.12.29 x8 + 28x2 + 20 2 8 1 12 $\textrm{GL(2,3)}$ (as 8T23) $ [4/3, 4/3, 2]_{3}^{2}$
2.8.12.3 x8 + 2x6 + 16x2 + 16 2 2 4 12 $C_2^2:C_4$ (as 8T10) $ [2, 3]^{4}$
2.8.12.30 x8 + 12x2 + 20 2 8 1 12 $\textrm{GL(2,3)}$ (as 8T23) $ [4/3, 4/3, 2]_{3}^{2}$
2.8.12.4 x8 + 2x6 + 16 2 2 4 12 $C_2^3: C_4$ (as 8T20) $ [2, 2, 3]^{4}$
2.8.12.5 x8 + 6x6 + 8x5 + 80 2 2 4 12 $C_8$ (as 8T1) $ [3]^{4}$
2.8.12.6 x8 + 2x6 + 8x4 + 80 2 2 4 12 $C_8$ (as 8T1) $ [3]^{4}$
2.8.12.7 x8 + 4x6 + 8x2 + 80 2 2 4 12 $C_8:C_2$ (as 8T7) $ [2, 3]^{4}$
2.8.12.8 x8 + 2x6 + 80 2 2 4 12 $(C_8:C_2):C_2$ (as 8T16) $ [2, 2, 3]^{4}$
2.8.12.9 x8 + 6x6 + 112 2 2 4 12 $((C_8 : C_2):C_2):C_2$ (as 8T27) $ [2, 2, 2, 3]^{4}$
2.8.14.1 x8 + 2x7 + 6 2 8 1 14 $A_4\times C_2$ (as 8T13) $ [2, 2, 2]^{3}$
2.8.14.10 x8 + 4x2 + 28 2 8 1 14 $C_2 \wr S_4$ (as 8T44) $ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$
2.8.14.11 x8 + 20x2 + 12 2 8 1 14 $C_2 \wr S_4$ (as 8T44) $ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$
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