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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
17.8.0.1 | x8 + 11x4 + 12x3 + 6x + 3 | $17$ | $1$ | $8$ | $0$ | $C_8$ (as 8T1) | $[\ ]^{8}$ |
17.8.4.1 | x8 + 612x7 + 140536x6 + 14363966x5 + 553913435x4 + 345855654x3 + 4032327212x2 + 6379401496x + 2294776272 | $17$ | $2$ | $4$ | $4$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{2}^{4}$ |
17.8.4.2 | x8 + 2023x4 - 49130x2 + 250563 | $17$ | $2$ | $4$ | $4$ | $C_8$ (as 8T1) | $[\ ]_{2}^{4}$ |
17.8.6.1 | x8 + 64x7 + 1548x6 + 16960x5 + 74840x4 + 51968x3 + 39432x2 + 270464x + 1062564 | $17$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{4}^{2}$ |
17.8.6.2 | x8 + 204x4 - 7225 | $17$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $[\ ]_{4}^{2}$ |
17.8.6.3 | x8 - 272x4 + 867 | $17$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $[\ ]_{4}^{2}$ |
17.8.6.4 | x8 - 3604x4 - 719321 | $17$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $[\ ]_{4}^{2}$ |
17.8.7.1 | x8 + 68 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.2 | x8 + 136 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.3 | x8 + 17 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.4 | x8 + 34 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.5 | x8 + 119 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.6 | x8 + 102 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.7 | x8 + 51 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |
17.8.7.8 | x8 + 85 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $[\ ]_{8}$ |