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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
17.6.0.1 | x6 - x + 12 | $17$ | $1$ | $6$ | $0$ | $C_6$ (as 6T1) | $ [\ ]^{6}$ |
17.6.3.1 | x6 - 34x4 + 289x2 - 44217 | $17$ | $2$ | $3$ | $3$ | $C_6$ (as 6T1) | $ [\ ]_{2}^{3}$ |
17.6.3.2 | x6 - 289x2 + 14739 | $17$ | $2$ | $3$ | $3$ | $C_6$ (as 6T1) | $ [\ ]_{2}^{3}$ |
17.6.4.1 | x6 + 136x3 + 7803 | $17$ | $3$ | $2$ | $4$ | $S_3$ (as 6T2) | $ [\ ]_{3}^{2}$ |
17.6.4.2 | x6 - 17x3 + 867 | $17$ | $3$ | $2$ | $4$ | $S_3\times C_3$ (as 6T5) | $ [\ ]_{3}^{6}$ |
17.6.5.1 | x6 - 17 | $17$ | $6$ | $1$ | $5$ | $D_{6}$ (as 6T3) | $ [\ ]_{6}^{2}$ |
17.6.5.2 | x6 + 51 | $17$ | $6$ | $1$ | $5$ | $D_{6}$ (as 6T3) | $ [\ ]_{6}^{2}$ |