| 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) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + t^{6} + t^{5} + t^{3} + t^{2} + t + 1$ |
$x - 2$ |
$[0]$ |
$[\ ]$ |
| 2.10.8.1 |
$10$ |
$x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 55 x^{5} + 55 x^{4} + 10 x^{3} - 25 x^{2} - 5 x + 7$ |
$2$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + t + 1$ |
$x^{5} + 2$ |
$[0]$ |
$[2]$ |
| 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) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.10.10.2 |
$10$ |
$x^{10} + 4 x^{9} + 46 x^{8} + 328 x^{7} + 1232 x^{6} + 4048 x^{5} + 5824 x^{4} + 6496 x^{3} - 8272 x^{2} - 14336 x - 17632$ |
$2$ |
$2$ |
$5$ |
$10$ |
$C_2^4 : C_5$ (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) |
$5$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2\right) x + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$4$ |
$5$ |
$[6/5]$ |
$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1, 4]$ |
| 2.10.12.1 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
| 2.10.12.2 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
| 2.10.12.3 |
$10$ |
$x^{10} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
| 2.10.12.4 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$10$ |
$1$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[8/5]$ |
$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 4]$ |
| 2.10.14.1 |
$10$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.2 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.3 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.4 |
$10$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.5 |
$10$ |
$x^{10} + 2 x^{5} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.6 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.7 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2$ |
$[5, 0]$ |
$[1, 4]$ |
| 2.10.14.8 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{4} + 6$ |
$2$ |
$10$ |
$1$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{4} + 6$ |
$[5, 0]$ |
$[1, 4]$ |
| 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) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.2 |
$10$ |
$x^{10} + 8 x^{9} + 102 x^{8} + 832 x^{7} + 6440 x^{6} + 35904 x^{5} + 191792 x^{4} + 594688 x^{3} + 1067088 x^{2} + 999040 x + 445152$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t + 4\right) x + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.3 |
$10$ |
$x^{10} - 12 x^{9} + 82 x^{8} - 32 x^{7} + 1976 x^{6} + 8544 x^{5} + 38064 x^{4} + 155008 x^{3} + 517392 x^{2} + 885056 x + 574496$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t\right) x + 12 t^{4} + 4 t^{3} + 4 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.4 |
$10$ |
$x^{10} + 14 x^{8} + 952 x^{6} + 15696 x^{4} + 92432 x^{2} + 183776$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 4 t^{4} + 12 t^{3} + 12 t^{2} + 8 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.6 |
$10$ |
$x^{10} - 12 x^{9} + 34 x^{8} + 1040 x^{7} - 168 x^{6} + 19712 x^{5} - 16464 x^{4} + 66752 x^{3} - 45424 x^{2} + 23232 x - 17632$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 4 t^{3} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.7 |
$10$ |
$x^{10} + 62 x^{8} - 96 x^{7} + 840 x^{6} + 64 x^{5} + 22832 x^{4} + 70528 x^{3} + 199632 x^{2} + 445184 x + 361824$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t\right) x + 8 t^{4} + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.8 |
$10$ |
$x^{10} + 20 x^{9} + 234 x^{8} + 2512 x^{7} + 17000 x^{6} + 100480 x^{5} + 430224 x^{4} + 1312448 x^{3} + 2519632 x^{2} + 2593984 x + 1080096$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{2} + 4 t + 4\right) x + 12 t^{4} + 4 t^{3} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 4 x + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.10 |
$10$ |
$x^{10} - 12 x^{9} + 110 x^{8} - 416 x^{7} + 4264 x^{6} - 11936 x^{5} + 27504 x^{4} - 98432 x^{3} + 20560 x^{2} - 83648 x + 9568$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t\right) x + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.11 |
$10$ |
$x^{10} + 20 x^{9} + 222 x^{8} + 1632 x^{7} + 8392 x^{6} + 35680 x^{5} + 129840 x^{4} + 366464 x^{3} + 703952 x^{2} + 802624 x + 377696$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 8 t^{4} + 8 t^{3} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.12 |
$10$ |
$x^{10} - 12 x^{9} + 30 x^{8} - 96 x^{7} + 2440 x^{6} + 5728 x^{5} + 31664 x^{4} + 22656 x^{3} + 16080 x^{2} + 26944 x + 9568$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3}\right) x + 8 t^{3} + 14$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$5$ |
$1$ |
$[3]$ |
$[3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{4} + 4 t^{3} + 12 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.14 |
$10$ |
$x^{10} - 12 x^{9} + 54 x^{8} - 320 x^{7} + 3784 x^{6} + 6816 x^{5} + 104176 x^{4} + 90624 x^{3} + 798672 x^{2} + 117824 x + 1510112$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3}\right) x + 8 t^{4} + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.15 |
$10$ |
$x^{10} - 12 x^{9} + 70 x^{8} + 32 x^{7} + 1832 x^{6} + 2528 x^{5} - 9424 x^{4} - 73600 x^{3} - 157616 x^{2} - 129216 x - 23328$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t\right) x + 8 t^{4} + 8 t^{3} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.10.15.16 |
$10$ |
$x^{10} + 20 x^{9} + 182 x^{8} + 992 x^{7} + 3336 x^{6} + 10848 x^{5} + 51312 x^{4} + 168320 x^{3} + 262864 x^{2} + 156480 x - 23328$ |
$2$ |
$2$ |
$5$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 8 t^{4} + 8 t^{3} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.10.16.1 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$10$ |
$1$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[12/5]$ |
$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$ |
$[7, 0]$ |
$[1, 4]$ |
| 2.10.16.2 |
$10$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$10$ |
$1$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[12/5]$ |
$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$ |
$[7, 0]$ |
$[1, 4]$ |
| 2.10.16.3 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$ |
$2$ |
$10$ |
$1$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[12/5]$ |
$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$ |
$[7, 0]$ |
$[1, 4]$ |
| 2.10.16.4 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$ |
$2$ |
$10$ |
$1$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[12/5]$ |
$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$ |
$[7, 0]$ |
$[1, 4]$ |
