| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 19.10.0.1 |
$10$ |
$x^{10} + 18 x^{5} + 13 x^{4} + 17 x^{3} + 3 x^{2} + 4 x + 2$ |
$19$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + 18 t^{5} + 13 t^{4} + 17 t^{3} + 3 t^{2} + 4 t + 2$ |
$x - 19$ |
$[0]$ |
$[\ ]$ |
| 19.10.5.1 |
$10$ |
$x^{10} + 651605 x^{2} - 42093683$ |
$19$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 5 t + 17$ |
$x^{2} + 19 t$ |
$[0]$ |
$[1]$ |
| 19.10.5.2 |
$10$ |
$x^{10} + 95 x^{8} + 3620 x^{6} + 34 x^{5} + 67640 x^{4} - 6460 x^{3} + 633580 x^{2} + 61540 x + 2545453$ |
$19$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 5 t + 17$ |
$x^{2} + 19$ |
$[0]$ |
$[1]$ |
| 19.10.8.1 |
$10$ |
$x^{10} + 90 x^{9} + 3250 x^{8} + 59040 x^{7} + 544360 x^{6} + 2125046 x^{5} + 1090430 x^{4} + 296960 x^{3} + 1113560 x^{2} + 9728680 x + 34800945$ |
$19$ |
$5$ |
$2$ |
$8$ |
$D_5$ (as 10T2) |
$2$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{2}$ |
$t^{2} + 18 t + 2$ |
$x^{5} + 19$ |
$[0]$ |
$[1]$ |
| 19.10.8.2 |
$10$ |
$x^{10} - 5396 x^{5} - 21660$ |
$19$ |
$5$ |
$2$ |
$8$ |
$D_5\times C_5$ (as 10T6) |
$10$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{10}$ |
$t^{2} + 18 t + 2$ |
$x^{5} + 304 t + 38$ |
$[0]$ |
$[1]$ |
| 19.10.8.3 |
$10$ |
$x^{10} - 5510 x^{5} - 1650131$ |
$19$ |
$5$ |
$2$ |
$8$ |
$D_5\times C_5$ (as 10T6) |
$10$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{10}$ |
$t^{2} + 18 t + 2$ |
$x^{5} + 342 t + 323$ |
$[0]$ |
$[1]$ |
| 19.10.9.1 |
$10$ |
$x^{10} + 38$ |
$19$ |
$10$ |
$1$ |
$9$ |
$D_{10}$ (as 10T3) |
$2$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{2}$ |
$t + 17$ |
$x^{10} + 38$ |
$[0]$ |
$[2]$ |
| 19.10.9.2 |
$10$ |
$x^{10} + 19$ |
$19$ |
$10$ |
$1$ |
$9$ |
$D_{10}$ (as 10T3) |
$2$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{2}$ |
$t + 17$ |
$x^{10} + 19$ |
$[0]$ |
$[2]$ |
