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| Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
|---|---|---|---|---|---|---|---|
| 7.8.0.1 | x8 - x + 3 | $7$ | $1$ | $8$ | $0$ | $C_8$ (as 8T1) | $ [\ ]^{8}$ |
| 7.8.4.1 | x8 + 14x6 + 539x4 + 343x2 + 60025 | $7$ | $2$ | $4$ | $4$ | $C_4\times C_2$ (as 8T2) | $ [\ ]_{2}^{4}$ |
| 7.8.4.2 | x8 + 49x4 - 1029x2 + 12005 | $7$ | $2$ | $4$ | $4$ | $C_8$ (as 8T1) | $ [\ ]_{2}^{4}$ |
| 7.8.6.1 | x8 + 35x4 + 441 | $7$ | $4$ | $2$ | $6$ | $Q_8$ (as 8T5) | $ [\ ]_{4}^{2}$ |
| 7.8.6.2 | x8 - 49x4 + 3969 | $7$ | $4$ | $2$ | $6$ | $D_4$ (as 8T4) | $ [\ ]_{4}^{2}$ |
| 7.8.6.3 | x8 - 7x4 + 147 | $7$ | $4$ | $2$ | $6$ | $C_8:C_2$ (as 8T7) | $ [\ ]_{4}^{4}$ |
| 7.8.7.1 | x8 + 14 | $7$ | $8$ | $1$ | $7$ | $D_{8}$ (as 8T6) | $ [\ ]_{8}^{2}$ |
| 7.8.7.2 | x8 - 7 | $7$ | $8$ | $1$ | $7$ | $D_{8}$ (as 8T6) | $ [\ ]_{8}^{2}$ |