| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.10.10.1 |
$10$ |
$x^{10} + 4 x^{9} + 6 x^{8} + 80 x^{7} + 616 x^{6} + 2352 x^{5} + 6000 x^{4} + 11136 x^{3} + 13776 x^{2} + 9472 x + 2784$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.10 |
$10$ |
$x^{10} + 10 x^{9} + 22 x^{8} + 160 x^{6} + 1200 x^{5} + 3168 x^{4} + 4480 x^{3} + 3760 x^{2} + 1824 x + 416$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{4} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.12 |
$10$ |
$x^{10} + 10 x^{9} + 34 x^{8} + 112 x^{7} + 328 x^{6} + 640 x^{5} + 1360 x^{4} + 2176 x^{3} + 1168 x^{2} + 1888 x - 1248$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.13 |
$10$ |
$x^{10} + 10 x^{9} + 10 x^{8} + 56 x^{7} + 192 x^{6} + 800 x^{5} + 1536 x^{4} + 2208 x^{3} + 2224 x^{2} + 96 x - 1056$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.14 |
$10$ |
$x^{10} + 4 x^{9} - 6 x^{8} + 176 x^{7} + 848 x^{6} + 2256 x^{5} + 1216 x^{4} - 1088 x^{3} - 5392 x^{2} - 5120 x - 3616$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2\right) x + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.15 |
$10$ |
$x^{10} + 2 x + 2$ |
$2$ |
$10$ |
$1$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[6/5]$ |
$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x + 2$ |
$[1, 0]$ |
$[1, 4]$ |
| 2.10.10.16 |
$10$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$2$ |
$10$ |
$1$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[6/5]$ |
$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1, 4]$ |
| 2.10.10.2 |
$10$ |
$x^{10} + 4 x^{9} + 46 x^{8} + 328 x^{7} + 1232 x^{6} + 4048 x^{5} + 5824 x^{4} + 6496 x^{3} - 8272 x^{2} - 14336 x - 17632$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{3} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.3 |
$10$ |
$x^{10} + 10 x^{9} + 74 x^{8} + 320 x^{7} + 1104 x^{6} + 2752 x^{5} + 6176 x^{4} + 12096 x^{3} + 17712 x^{2} + 15968 x + 8416$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t + 2\right) x + 4 t^{4} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.4 |
$10$ |
$x^{10} - 2 x^{8} + 16 x^{7} - 8 x^{6} - 432 x^{5} - 176 x^{4} - 960 x^{3} - 1776 x^{2} - 448 x - 32$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 t x + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.5 |
$10$ |
$x^{10} + 34 x^{8} - 24 x^{7} + 368 x^{6} - 496 x^{5} + 1568 x^{4} - 1760 x^{3} + 2992 x^{2} - 1856 x + 352$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t\right) x + 4 t^{4} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.6 |
$10$ |
$x^{10} - 6 x^{9} + 42 x^{8} - 104 x^{7} - 256 x^{6} - 112 x^{5} - 1568 x^{4} - 2016 x^{3} - 2832 x^{2} - 4960 x - 3616$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{10}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.8 |
$10$ |
$x^{10} + 4 x^{9} + 14 x^{8} + 240 x^{7} + 928 x^{6} + 4400 x^{5} + 6368 x^{4} + 13888 x^{3} - 336 x^{2} + 2432 x - 17632$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2\right) x + 4 t^{3} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.9 |
$10$ |
$x^{10} + 10 x^{9} + 22 x^{8} - 8 x^{7} + 72 x^{6} + 1328 x^{5} + 4496 x^{4} + 3680 x^{3} - 3696 x^{2} - 96 x - 32$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2\right) x + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
