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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
5.8.0.1 | x8 + x4 + 3x2 + 4x + 2 | $5$ | $1$ | $8$ | $0$ | $C_8$ (as 8T1) | $[\ ]^{8}$ |
5.8.4.1 | x8 + 80x7 + 2428x6 + 33688x5 + 195810x4 + 305952x3 + 870132x2 + 1037416x + 503089 | $5$ | $2$ | $4$ | $4$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{2}^{4}$ |
5.8.4.2 | x8 + 100x4 - 500x2 + 1250 | $5$ | $2$ | $4$ | $4$ | $C_8$ (as 8T1) | $[\ ]_{2}^{4}$ |
5.8.6.1 | x8 + 16x7 + 104x6 + 352x5 + 674x4 + 784x3 + 776x2 + 928x + 721 | $5$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{4}^{2}$ |
5.8.6.2 | x8 + 10x4 - 25 | $5$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{4}^{2}$ |
5.8.6.3 | x8 - 50x4 - 175 | $5$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $[\ ]_{4}^{2}$ |
5.8.6.4 | x8 - 20x4 + 50 | $5$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $[\ ]_{4}^{2}$ |
5.8.7.1 | x8 + 20 | $5$ | $8$ | $1$ | $7$ | $C_8:C_2$ (as 8T7) | $[\ ]_{8}^{2}$ |
5.8.7.2 | x8 + 5 | $5$ | $8$ | $1$ | $7$ | $C_8:C_2$ (as 8T7) | $[\ ]_{8}^{2}$ |
5.8.7.3 | x8 + 10 | $5$ | $8$ | $1$ | $7$ | $C_8:C_2$ (as 8T7) | $[\ ]_{8}^{2}$ |
5.8.7.4 | x8 + 15 | $5$ | $8$ | $1$ | $7$ | $C_8:C_2$ (as 8T7) | $[\ ]_{8}^{2}$ |