| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.10.0.1 |
$10$ |
$x^{10} + x^{6} + x^{5} + x^{3} + x^{2} + x + 1$ |
$2$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + t^{6} + t^{5} + t^{3} + t^{2} + t + 1$ |
$x - 2$ |
$[0]$ |
$[]$ |
| 2.10.10.11 |
$10$ |
$x^{10} + 10 x^{9} + 38 x^{8} + 64 x^{7} + 152 x^{6} + 688 x^{5} + 912 x^{4} - 1024 x^{3} - 1968 x^{2} + 32 x - 32$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.7 |
$10$ |
$x^{10} + 10 x^{9} + 50 x^{8} + 160 x^{7} + 360 x^{6} + 592 x^{5} + 656 x^{4} + 384 x^{3} - 112 x^{2} - 352 x - 1248$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.15.1 |
$10$ |
$x^{10} + 70 x^{8} + 2 x^{7} + 1960 x^{6} - 26 x^{5} + 27441 x^{4} - 2240 x^{3} + 192110 x^{2} - 14504 x + 537993$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.13 |
$10$ |
$x^{10} - 12 x^{9} + 174 x^{8} - 640 x^{7} - 40 x^{6} + 11424 x^{5} - 7984 x^{4} - 79360 x^{3} + 84112 x^{2} + 955968 x + 1404384$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{4} + 4 t^{3} + 12 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.5 |
$10$ |
$x^{10} + 46 x^{8} + 808 x^{6} + 6768 x^{4} + 27216 x^{2} + 9568$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.9 |
$10$ |
$x^{10} + 20 x^{9} + 206 x^{8} + 1376 x^{7} + 6504 x^{6} + 22496 x^{5} + 57328 x^{4} + 105856 x^{3} + 135504 x^{2} + 108864 x + 9568$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 4 x + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
