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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
7.8.0.1 | x8 + 4x3 + 6x2 + 2x + 3 | $7$ | $1$ | $8$ | $0$ | $C_8$ (as 8T1) | $[\ ]^{8}$ |
7.8.4.1 | x8 + 38x6 + 8x5 + 395x4 - 72x3 + 1026x2 - 872x + 401 | $7$ | $2$ | $4$ | $4$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{2}^{4}$ |
7.8.4.2 | x8 + 245x4 - 1372x2 + 7203 | $7$ | $2$ | $4$ | $4$ | $C_8$ (as 8T1) | $[\ ]_{2}^{4}$ |
7.8.6.1 | x8 + 14x4 - 245 | $7$ | $4$ | $2$ | $6$ | $Q_8$ (as 8T5) | $[\ ]_{4}^{2}$ |
7.8.6.2 | x8 + 24x7 + 228x6 + 1080x5 + 2660x4 + 3408x3 + 3312x2 + 5184x + 6304 | $7$ | $4$ | $2$ | $6$ | $D_4$ (as 8T4) | $[\ ]_{4}^{2}$ |
7.8.6.3 | x8 - 154x4 - 1421 | $7$ | $4$ | $2$ | $6$ | $C_8:C_2$ (as 8T7) | $[\ ]_{4}^{4}$ |
7.8.7.1 | x8 + 7 | $7$ | $8$ | $1$ | $7$ | $D_{8}$ (as 8T6) | $[\ ]_{8}^{2}$ |
7.8.7.2 | x8 + 21 | $7$ | $8$ | $1$ | $7$ | $D_{8}$ (as 8T6) | $[\ ]_{8}^{2}$ |