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| Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
|---|---|---|---|---|---|---|---|
| 17.8.0.1 | x8 + x2 - 3x + 3 | $17$ | $1$ | $8$ | $0$ | $C_8$ (as 8T1) | $ [\ ]^{8}$ |
| 17.8.4.1 | x8 + 6358x4 - 4913x2 + 10106041 | $17$ | $2$ | $4$ | $4$ | $C_4\times C_2$ (as 8T2) | $ [\ ]_{2}^{4}$ |
| 17.8.4.2 | x8 - 4913x2 + 918731 | $17$ | $2$ | $4$ | $4$ | $C_8$ (as 8T1) | $ [\ ]_{2}^{4}$ |
| 17.8.6.1 | x8 - 119x4 + 23409 | $17$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $ [\ ]_{4}^{2}$ |
| 17.8.6.2 | x8 + 85x4 + 2601 | $17$ | $4$ | $2$ | $6$ | $C_4\times C_2$ (as 8T2) | $ [\ ]_{4}^{2}$ |
| 17.8.6.3 | x8 - 17x4 + 867 | $17$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $ [\ ]_{4}^{2}$ |
| 17.8.6.4 | x8 + 136x4 + 7803 | $17$ | $4$ | $2$ | $6$ | $C_8$ (as 8T1) | $ [\ ]_{4}^{2}$ |
| 17.8.7.1 | x8 - 1377 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.2 | x8 - 153 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.3 | x8 - 17 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.4 | x8 - 12393 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.5 | x8 + 459 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.6 | x8 + 37179 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.7 | x8 + 51 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |
| 17.8.7.8 | x8 + 4131 | $17$ | $8$ | $1$ | $7$ | $C_8$ (as 8T1) | $ [\ ]_{8}$ |