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Label | Polynomial | $p$ | $e$ | $f$ | $c$ | Galois group | Slope content |
---|---|---|---|---|---|---|---|
19.10.0.1 | x10 + 18x5 + 13x4 + 17x3 + 3x2 + 4x + 2 | $19$ | $1$ | $10$ | $0$ | $C_{10}$ (as 10T1) | $[\ ]^{10}$ |
19.10.5.1 | x10 + 651605x2 - 42093683 | $19$ | $2$ | $5$ | $5$ | $C_{10}$ (as 10T1) | $[\ ]_{2}^{5}$ |
19.10.5.2 | x10 + 95x8 + 3620x6 + 34x5 + 67640x4 - 6460x3 + 633580x2 + 61540x + 2545453 | $19$ | $2$ | $5$ | $5$ | $C_{10}$ (as 10T1) | $[\ ]_{2}^{5}$ |
19.10.8.1 | x10 + 90x9 + 3250x8 + 59040x7 + 544360x6 + 2125046x5 + 1090430x4 + 296960x3 + 1113560x2 + 9728680x + 34800945 | $19$ | $5$ | $2$ | $8$ | $D_5$ (as 10T2) | $[\ ]_{5}^{2}$ |
19.10.8.2 | x10 - 5396x5 - 21660 | $19$ | $5$ | $2$ | $8$ | $D_5\times C_5$ (as 10T6) | $[\ ]_{5}^{10}$ |
19.10.8.3 | x10 - 5510x5 - 1650131 | $19$ | $5$ | $2$ | $8$ | $D_5\times C_5$ (as 10T6) | $[\ ]_{5}^{10}$ |
19.10.9.1 | x10 + 38 | $19$ | $10$ | $1$ | $9$ | $D_{10}$ (as 10T3) | $[\ ]_{10}^{2}$ |
19.10.9.2 | x10 + 19 | $19$ | $10$ | $1$ | $9$ | $D_{10}$ (as 10T3) | $[\ ]_{10}^{2}$ |