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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
5.6.0.1 | x6 + x4 + 4x3 + x2 + 2 | $5$ | $1$ | $6$ | $0$ | $C_6$ (as 6T1) | $[\ ]^{6}$ |
5.6.3.1 | x6 + 60x5 + 1221x4 + 8846x3 + 9864x2 + 29208x + 29309 | $5$ | $2$ | $3$ | $3$ | $C_6$ (as 6T1) | $[\ ]_{2}^{3}$ |
5.6.3.2 | x6 + 75x2 - 375 | $5$ | $2$ | $3$ | $3$ | $C_6$ (as 6T1) | $[\ ]_{2}^{3}$ |
5.6.4.1 | x6 + 12x5 + 54x4 + 122x3 + 168x2 + 228x + 233 | $5$ | $3$ | $2$ | $4$ | $S_3$ (as 6T2) | $[\ ]_{3}^{2}$ |
5.6.4.2 | x6 + 10x3 - 25 | $5$ | $3$ | $2$ | $4$ | $S_3\times C_3$ (as 6T5) | $[\ ]_{3}^{6}$ |
5.6.5.1 | x6 + 5 | $5$ | $6$ | $1$ | $5$ | $D_{6}$ (as 6T3) | $[\ ]_{6}^{2}$ |
5.6.5.2 | x6 + 10 | $5$ | $6$ | $1$ | $5$ | $D_{6}$ (as 6T3) | $[\ ]_{6}^{2}$ |