| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.10.8.1 |
$10$ |
$x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 55 x^{5} + 55 x^{4} + 10 x^{3} - 25 x^{2} - 5 x + 7$ |
$2$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + t + 1$ |
$x^{5} + 2$ |
$[0]$ |
$[2]$ |
| 3.10.8.1 |
$10$ |
$x^{10} + 10 x^{9} + 50 x^{8} + 160 x^{7} + 360 x^{6} + 598 x^{5} + 750 x^{4} + 640 x^{3} + 280 x^{2} + 40 x + 17$ |
$3$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{5} + 3$ |
$[0]$ |
$[2]$ |
| 5.10.11.1 |
$10$ |
$x^{10} + 20 x^{2} + 5$ |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{10} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
| 5.10.11.2 |
$10$ |
$x^{10} + 5 x^{2} + 5$ |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
| 5.10.11.5 |
$10$ |
$x^{10} + 15 x^{2} + 10$ |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{2} + 10$ |
$[2, 0]$ |
$[1, 1]$ |
| 5.10.11.6 |
$10$ |
$x^{10} + 10 x^{2} + 10$ |
$5$ |
$10$ |
$1$ |
$11$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{10} + 10 x^{2} + 10$ |
$[2, 0]$ |
$[1, 1]$ |
| 5.10.12.8 |
$10$ |
$x^{10} - 50 x^{8} + 40 x^{7} - 175 x^{6} - 990 x^{5} + 400 x^{4} - 250 x^{3} + 200 x^{2} + 25$ |
$5$ |
$5$ |
$2$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(20 t + 15\right) x^{3} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.10.12.9 |
$10$ |
$x^{10} + 10 x^{7} - 50 x^{6} + 10 x^{5} + 25 x^{4} + 50 x^{2} + 25$ |
$5$ |
$5$ |
$2$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 10\right) x^{3} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.10.15.1 |
$10$ |
$x^{10} + 15 x^{6} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{10} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.13 |
$10$ |
$x^{10} + 5 x^{6} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{10} + 5 x^{6} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.14 |
$10$ |
$x^{10} + 20 x^{6} + 10$ |
$5$ |
$10$ |
$1$ |
$15$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{10} + 20 x^{6} + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.15.2 |
$10$ |
$x^{10} + 10 x^{6} + 5$ |
$5$ |
$10$ |
$1$ |
$15$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{10} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
| 5.10.16.13 |
$10$ |
$x^{10} + 50 x^{9} + 935 x^{8} + 8480 x^{7} + 42480 x^{6} + 124364 x^{5} + 216420 x^{4} + 227120 x^{3} + 168160 x^{2} + 129680 x + 80612$ |
$5$ |
$5$ |
$2$ |
$16$ |
$F_5$ (as 10T4) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 15 x^{4} + 30$ |
$[4, 0]$ |
$[2]$ |
| 5.10.16.14 |
$10$ |
$x^{10} + 20 x^{9} + 100 x^{8} - 390 x^{5} - 3900 x^{4} + 18025$ |
$5$ |
$5$ |
$2$ |
$16$ |
$F_5$ (as 10T4) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 x^{4} + 100 t + 5$ |
$[4, 0]$ |
$[2]$ |
| 5.10.19.1 |
$10$ |
$x^{10} + 5$ |
$5$ |
$10$ |
$1$ |
$19$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{10} + 5$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.2 |
$10$ |
$x^{10} + 25 x^{2} + 55$ |
$5$ |
$10$ |
$1$ |
$19$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{10} + 25 x^{2} + 55$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.3 |
$10$ |
$x^{10} + 50 x^{2} + 105$ |
$5$ |
$10$ |
$1$ |
$19$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{10} + 50 x^{2} + 105$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.4 |
$10$ |
$x^{10} + 75 x^{2} + 30$ |
$5$ |
$10$ |
$1$ |
$19$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{10} + 75 x^{2} + 30$ |
$[10, 0]$ |
$[1, 1]$ |
| 5.10.19.5 |
$10$ |
$x^{10} + 100 x^{2} + 80$ |
$5$ |
$10$ |
$1$ |
$19$ |
$F_5$ (as 10T4) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{10} + 100 x^{2} + 80$ |
$[10, 0]$ |
$[1, 1]$ |
| 7.10.8.1 |
$10$ |
$x^{10} + 30 x^{9} + 375 x^{8} + 2520 x^{7} + 9810 x^{6} + 22370 x^{5} + 29640 x^{4} + 24780 x^{3} + 21465 x^{2} + 33300 x + 33934$ |
$7$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 6 t + 3$ |
$x^{5} + 7$ |
$[0]$ |
$[2]$ |
| 13.10.8.1 |
$10$ |
$x^{10} + 60 x^{9} + 1450 x^{8} + 17760 x^{7} + 112360 x^{6} + 319418 x^{5} + 225500 x^{4} + 89240 x^{3} + 226880 x^{2} + 1274440 x + 3013497$ |
$13$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 12 t + 2$ |
$x^{5} + 13$ |
$[0]$ |
$[2]$ |
| 17.10.8.1 |
$10$ |
$x^{10} + 80 x^{9} + 2575 x^{8} + 41920 x^{7} + 350810 x^{6} + 1298690 x^{5} + 1053790 x^{4} + 419780 x^{3} + 741365 x^{2} + 5317450 x + 16794084$ |
$17$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 16 t + 3$ |
$x^{5} + 17$ |
$[0]$ |
$[2]$ |
| 23.10.8.1 |
$10$ |
$x^{10} + 105 x^{9} + 4435 x^{8} + 94710 x^{7} + 1038805 x^{6} + 5025997 x^{5} + 5196440 x^{4} + 2466880 x^{3} + 2611955 x^{2} + 21422390 x + 88673277$ |
$23$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 21 t + 5$ |
$x^{5} + 23$ |
$[0]$ |
$[2]$ |
| 37.10.8.1 |
$10$ |
$x^{10} + 165 x^{9} + 10900 x^{8} + 360690 x^{7} + 5994985 x^{6} + 40576907 x^{5} + 11996075 x^{4} + 1844210 x^{3} + 13310630 x^{2} + 217787785 x + 1434738672$ |
$37$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 33 t + 2$ |
$x^{5} + 37$ |
$[0]$ |
$[2]$ |
| 43.10.8.1 |
$10$ |
$x^{10} + 210 x^{9} + 17655 x^{8} + 743400 x^{7} + 15717330 x^{6} + 135147938 x^{5} + 47161020 x^{4} + 7446540 x^{3} + 32171985 x^{2} + 664484400 x + 5572019578$ |
$43$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 42 t + 3$ |
$x^{5} + 43$ |
$[0]$ |
$[2]$ |
| 47.10.8.1 |
$10$ |
$x^{10} + 225 x^{9} + 20275 x^{8} + 915750 x^{7} + 20807125 x^{6} + 193674469 x^{5} + 104046200 x^{4} + 23840800 x^{3} + 45045875 x^{2} + 954281750 x + 8566019709$ |
$47$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 45 t + 5$ |
$x^{5} + 47$ |
$[0]$ |
$[2]$ |
| 53.10.8.1 |
$10$ |
$x^{10} + 245 x^{9} + 24020 x^{8} + 1178450 x^{7} + 28968105 x^{6} + 287187195 x^{5} + 57949195 x^{4} + 5984210 x^{3} + 62390310 x^{2} + 1522588185 x + 14908889008$ |
$53$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 49 t + 2$ |
$x^{5} + 53$ |
$[0]$ |
$[2]$ |
| 67.10.8.1 |
$10$ |
$x^{10} + 315 x^{9} + 39700 x^{8} + 2502990 x^{7} + 79002985 x^{6} + 1002446117 x^{5} + 158027075 x^{4} + 12668510 x^{3} + 167595830 x^{2} + 5266612735 x + 66325805832$ |
$67$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 63 t + 2$ |
$x^{5} + 67$ |
$[0]$ |
$[2]$ |
| 73.10.8.1 |
$10$ |
$x^{10} + 350 x^{9} + 49025 x^{8} + 3437000 x^{7} + 120785250 x^{6} + 1715052646 x^{5} + 603951800 x^{4} + 89494700 x^{3} + 255751625 x^{2} + 8728117000 x + 122065772204$ |
$73$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 70 t + 5$ |
$x^{5} + 73$ |
$[0]$ |
$[2]$ |
| 83.10.8.1 |
$10$ |
$x^{10} + 410 x^{9} + 67250 x^{8} + 5516960 x^{7} + 226464360 x^{6} + 3729463158 x^{5} + 452962750 x^{4} + 27645440 x^{3} + 457765080 x^{2} + 18740739240 x + 307256577457$ |
$83$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 82 t + 2$ |
$x^{5} + 83$ |
$[0]$ |
$[2]$ |
| 97.10.8.1 |
$10$ |
$x^{10} + 480 x^{9} + 92185 x^{8} + 8856960 x^{7} + 426055930 x^{6} + 8242272770 x^{5} + 2130326210 x^{4} + 230353820 x^{3} + 868320245 x^{2} + 41104237210 x + 788767208406$ |
$97$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 96 t + 5$ |
$x^{5} + 97$ |
$[0]$ |
$[2]$ |
| 103.10.8.1 |
$10$ |
$x^{10} + 510 x^{9} + 104065 x^{8} + 10622280 x^{7} + 542776930 x^{6} + 11147005538 x^{5} + 2713937180 x^{4} + 276262820 x^{3} + 1104476465 x^{2} + 55638439540 x + 1134471943680$ |
$103$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 102 t + 5$ |
$x^{5} + 103$ |
$[0]$ |
$[2]$ |
| 107.10.8.1 |
$10$ |
$x^{10} + 515 x^{9} + 106100 x^{8} + 10931390 x^{7} + 563390985 x^{6} + 11636462397 x^{5} + 1126837075 x^{4} + 55072910 x^{3} + 1169405430 x^{2} + 60169327335 x + 1239254273512$ |
$107$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 103 t + 2$ |
$x^{5} + 107$ |
$[0]$ |
$[2]$ |
| 113.10.8.1 |
$10$ |
$x^{10} + 505 x^{9} + 102025 x^{8} + 10309070 x^{7} + 521220185 x^{6} + 10571946057 x^{5} + 1563717620 x^{4} + 104301980 x^{3} + 1165967635 x^{2} + 58725014860 x + 1185895523015$ |
$113$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 101 t + 3$ |
$x^{5} + 113$ |
$[0]$ |
$[2]$ |
| 127.10.8.1 |
$10$ |
$x^{10} + 630 x^{9} + 158775 x^{8} + 20011320 x^{7} + 1261665810 x^{6} + 31878026210 x^{5} + 3785077440 x^{4} + 200256780 x^{3} + 2543324265 x^{2} + 159929171100 x + 4029452130934$ |
$127$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 126 t + 3$ |
$x^{5} + 127$ |
$[0]$ |
$[2]$ |
| 137.10.8.1 |
$10$ |
$x^{10} + 655 x^{9} + 171625 x^{8} + 22488770 x^{7} + 1474044185 x^{6} + 38714410755 x^{5} + 4422222290 x^{4} + 225901280 x^{3} + 3082903315 x^{2} + 201591447850 x + 5280771081809$ |
$137$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 131 t + 3$ |
$x^{5} + 137$ |
$[0]$ |
$[2]$ |
| 157.10.8.1 |
$10$ |
$x^{10} + 760 x^{9} + 231065 x^{8} + 35133280 x^{7} + 2672439930 x^{6} + 81488107146 x^{5} + 13362318970 x^{4} + 914589580 x^{3} + 5538842085 x^{2} + 418666712010 x + 12724698653398$ |
$157$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 152 t + 5$ |
$x^{5} + 157$ |
$[0]$ |
$[2]$ |
| 163.10.8.1 |
$10$ |
$x^{10} + 795 x^{9} + 252820 x^{8} + 40203150 x^{7} + 3197161705 x^{6} + 101782311365 x^{5} + 6394452995 x^{4} + 202014110 x^{3} + 6552544310 x^{2} + 520725290335 x + 16557753750408$ |
$163$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 159 t + 2$ |
$x^{5} + 163$ |
$[0]$ |
$[2]$ |
| 167.10.8.1 |
$10$ |
$x^{10} + 830 x^{9} + 275585 x^{8} + 45759560 x^{7} + 3800799330 x^{6} + 126506855010 x^{5} + 19004135260 x^{4} + 1189990820 x^{3} + 7669364145 x^{2} + 633583543860 x + 21031139006656$ |
$167$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 166 t + 5$ |
$x^{5} + 167$ |
$[0]$ |
$[2]$ |
| 173.10.8.1 |
$10$ |
$x^{10} + 845 x^{9} + 285620 x^{8} + 48274850 x^{7} + 4080367305 x^{6} + 138051584835 x^{5} + 8160880795 x^{4} + 242503010 x^{3} + 8350910310 x^{2} + 705409451985 x + 23841169325008$ |
$173$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 169 t + 2$ |
$x^{5} + 173$ |
$[0]$ |
$[2]$ |
| 193.10.8.1 |
$10$ |
$x^{10} + 960 x^{9} + 368665 x^{8} + 70798080 x^{7} + 6800302330 x^{6} + 261627196418 x^{5} + 34001696930 x^{4} + 1841080220 x^{3} + 13700848565 x^{2} + 1310680261690 x + 50323271666550$ |
$193$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 192 t + 5$ |
$x^{5} + 193$ |
$[0]$ |
$[2]$ |
| 197.10.8.1 |
$10$ |
$x^{10} + 960 x^{9} + 368650 x^{8} + 70786560 x^{7} + 6796984360 x^{6} + 261202402186 x^{5} + 13594157840 x^{4} + 355760440 x^{3} + 13944119120 x^{2} + 1338279713480 x + 51387152212665$ |
$197$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 192 t + 2$ |
$x^{5} + 197$ |
$[0]$ |
$[2]$ |
