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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}$ |