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Label Polynomial $p$ $e$ $f$ $c$ Galois group Slope content
3.6.0.1 x6 - x + 2 $3$ $1$ $6$ $0$ $C_6$ (as 6T1) $ [\ ]^{6}$
3.6.3.1 x6 - 6x4 + 9x2 - 27 $3$ $2$ $3$ $3$ $C_6$ (as 6T1) $ [\ ]_{2}^{3}$
3.6.3.2 x6 - 9x2 + 27 $3$ $2$ $3$ $3$ $C_6$ (as 6T1) $ [\ ]_{2}^{3}$
3.6.6.1 x6 + 3x5 - 2 $3$ $3$ $2$ $6$ $C_3^2:C_4$ (as 6T10) $ [3/2, 3/2]_{2}^{2}$
3.6.6.2 x6 + 6x4 + 6x3 + 18 $3$ $3$ $2$ $6$ $C_3^2:C_4$ (as 6T10) $ [3/2, 3/2]_{2}^{2}$
3.6.6.3 x6 + 3x4 + 9 $3$ $3$ $2$ $6$ $D_{6}$ (as 6T3) $ [3/2]_{2}^{2}$
3.6.6.4 x6 + 3x4 + 6x3 + 9x2 + 63x + 9 $3$ $3$ $2$ $6$ $D_{6}$ (as 6T3) $ [3/2]_{2}^{2}$
3.6.6.5 x6 + 6x3 + 9x2 + 9 $3$ $3$ $2$ $6$ $S_3^2$ (as 6T9) $ [3/2, 3/2]_{2}^{2}$
3.6.6.6 x6 + 3x + 3 $3$ $6$ $1$ $6$ $C_3^2:D_4$ (as 6T13) $ [5/4, 5/4]_{4}^{2}$
3.6.6.7 x6 + 3x + 6 $3$ $6$ $1$ $6$ $C_3^2:D_4$ (as 6T13) $ [5/4, 5/4]_{4}^{2}$
3.6.7.1 x6 + 6x2 + 6 $3$ $6$ $1$ $7$ $S_3$ (as 6T2) $ [3/2]_{2}$
3.6.7.2 x6 + 3x2 + 6 $3$ $6$ $1$ $7$ $D_{6}$ (as 6T3) $ [3/2]_{2}^{2}$
3.6.7.3 x6 + 6x3 + 6x2 + 6 $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $ [3/2]_{2}^{3}$
3.6.7.4 x6 + 3x2 + 3 $3$ $6$ $1$ $7$ $S_3$ (as 6T2) $ [3/2]_{2}$
3.6.7.5 x6 + 6x2 + 3 $3$ $6$ $1$ $7$ $D_{6}$ (as 6T3) $ [3/2]_{2}^{2}$
3.6.7.6 x6 + 3x3 + 3x2 + 3 $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $ [3/2]_{2}^{3}$
3.6.8.1 x6 + 6x5 + 18x2 + 9 $3$ $3$ $2$ $8$ $C_3^2:C_4$ (as 6T10) $ [2, 2]^{4}$
3.6.8.10 x6 + 6x5 + 36 $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $ [2, 2]^{2}$
3.6.8.2 x6 + 6x5 + 9x2 + 9 $3$ $3$ $2$ $8$ $C_3^2:C_4$ (as 6T10) $ [2, 2]^{4}$
3.6.8.3 x6 + 18x2 + 9 $3$ $3$ $2$ $8$ $C_6$ (as 6T1) $ [2]^{2}$
3.6.8.4 x6 + 18x2 + 63 $3$ $3$ $2$ $8$ $C_6$ (as 6T1) $ [2]^{2}$
3.6.8.5 x6 + 9x2 + 9 $3$ $3$ $2$ $8$ $S_3$ (as 6T2) $ [2]^{2}$
3.6.8.6 x6 + 18x2 + 36 $3$ $3$ $2$ $8$ $C_6$ (as 6T1) $ [2]^{2}$
3.6.8.7 x6 + 6x5 + 6x3 + 72 $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $ [2]^{6}$
3.6.8.8 x6 + 3x5 + 63 $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $ [2, 2]^{2}$
3.6.8.9 x6 + 6x5 + 9 $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $ [2, 2]^{2}$
3.6.9.1 x6 + 3x4 + 15 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.9.10 x6 + 6x4 + 3 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.9.11 x6 + 6x4 + 12 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.9.12 x6 + 3x4 + 3 $3$ $6$ $1$ $9$ $D_{6}$ (as 6T3) $ [2]_{2}^{2}$
3.6.9.13 x6 + 6x5 + 6x4 + 21 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.14 x6 + 6x5 + 6x4 + 12 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.15 x6 + 6x4 + 6x3 + 12 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.16 x6 + 3x4 + 6x3 + 3 $3$ $6$ $1$ $9$ $S_3^2$ (as 6T9) $ [3/2, 2]_{2}^{2}$
3.6.9.2 x6 + 3x4 + 6 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.9.3 x6 + 3x4 + 24 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.9.4 x6 + 6x4 + 6 $3$ $6$ $1$ $9$ $D_{6}$ (as 6T3) $ [2]_{2}^{2}$
3.6.9.5 x6 + 3x4 + 3x3 + 15 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.6 x6 + 3x4 + 6x3 + 6 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.7 x6 + 6x5 + 3x4 + 15 $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $ [3/2, 2]_{2}$
3.6.9.8 x6 + 6x4 + 3x3 + 6 $3$ $6$ $1$ $9$ $S_3^2$ (as 6T9) $ [3/2, 2]_{2}^{2}$
3.6.9.9 x6 + 6x4 + 21 $3$ $6$ $1$ $9$ $C_6$ (as 6T1) $ [2]_{2}$
3.6.10.1 x6 - 18 $3$ $3$ $2$ $10$ $D_{6}$ (as 6T3) $ [5/2]_{2}^{2}$
3.6.10.10 x6 + 3x5 + 24 $3$ $6$ $1$ $10$ $C_3^2:D_4$ (as 6T13) $ [9/4, 9/4]_{4}^{2}$
3.6.10.11 x6 + 3x5 + 15 $3$ $6$ $1$ $10$ $C_3^2:D_4$ (as 6T13) $ [9/4, 9/4]_{4}^{2}$
3.6.10.12 x6 + 3x5 + 3 $3$ $6$ $1$ $10$ $C_3^2:D_4$ (as 6T13) $ [9/4, 9/4]_{4}^{2}$
3.6.10.2 x6 + 9 $3$ $3$ $2$ $10$ $D_{6}$ (as 6T3) $ [5/2]_{2}^{2}$
3.6.10.3 x6 + 36 $3$ $3$ $2$ $10$ $D_{6}$ (as 6T3) $ [5/2]_{2}^{2}$
3.6.10.4 x6 + 3x3 + 72 $3$ $3$ $2$ $10$ $S_3^2$ (as 6T9) $ [3/2, 5/2]_{2}^{2}$
3.6.10.5 x6 + 6x3 + 45 $3$ $3$ $2$ $10$ $S_3^2$ (as 6T9) $ [3/2, 5/2]_{2}^{2}$
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