Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.16.13 |
$12$ |
$x^{12} + 10 x^{11} + 47 x^{10} + 144 x^{9} + 330 x^{8} + 578 x^{7} + 785 x^{6} + 830 x^{5} + 530 x^{4} - 64 x^{3} - 189 x^{2} - 30 x + 25$ |
$2$ |
$6$ |
$2$ |
$16$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
2.12.22.60 |
$12$ |
$x^{12} + 14 x^{11} + 85 x^{10} + 314 x^{9} + 832 x^{8} + 1646 x^{7} + 2525 x^{6} + 2970 x^{5} + 2416 x^{4} + 910 x^{3} - 155 x^{2} - 150 x + 25$ |
$2$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[3]$ |
$[3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.79 |
$12$ |
$x^{12} - 4 x^{11} + 16 x^{10} - 4 x^{9} + 32 x^{8} + 32 x^{7} + 96 x^{5} - 4 x^{4} + 72 x^{3} + 88 x^{2} + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[3]$ |
$[3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 4 t x^{3} + \left(4 t + 2\right) x^{2} + 4 x + 12 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
3.12.14.11 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 792 x^{8} + 1728 x^{7} + 2918 x^{6} + 3684 x^{5} + 3156 x^{4} + 1376 x^{3} - 36 x^{2} - 168 x + 25$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
3.12.14.6 |
$12$ |
$x^{12} + 6 x^{8} + 15 x^{6} + 9 x^{4} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
3.12.18.85 |
$12$ |
$x^{12} + 24 x^{11} + 246 x^{10} + 1468 x^{9} + 5901 x^{8} + 17052 x^{7} + 36566 x^{6} + 58896 x^{5} + 70926 x^{4} + 62060 x^{3} + 37140 x^{2} + 13680 x + 2425$ |
$3$ |
$6$ |
$2$ |
$18$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 x^{4} + 6 x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
3.12.22.44 |
$12$ |
$x^{12} + 105 x^{6} + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 9\right) x^{3} + 12$ |
$[6, 0]$ |
$[1, 1]$ |
3.12.22.67 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 816 x^{8} + 1920 x^{7} + 3512 x^{6} + 4560 x^{5} + 3444 x^{4} + 272 x^{3} - 720 x^{2} + 960 x + 928$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{2} + 12$ |
$[6, 0]$ |
$[1, 1]$ |
3.12.22.96 |
$12$ |
$x^{12} + 30 x^{9} + 36 x^{7} + 231 x^{6} + 621 x^{4} + 90 x^{3} + 486 x^{2} + 108 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 15 x^{3} + \left(9 t + 9\right) x^{2} + 18 x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
5.12.10.1 |
$12$ |
$x^{12} + 20 x^{7} + 10 x^{6} + 50 x^{2} + 100 x + 25$ |
$5$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 4 t + 2$ |
$x^{6} + \left(5 t + 20\right) x + 5$ |
$[0]$ |
$[1]$ |
11.12.10.1 |
$12$ |
$x^{12} + 42 x^{11} + 747 x^{10} + 7280 x^{9} + 41955 x^{8} + 143682 x^{7} + 279531 x^{6} + 287826 x^{5} + 175245 x^{4} + 124460 x^{3} + 344757 x^{2} + 893466 x + 996620$ |
$11$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{6} + 11$ |
$[0]$ |
$[1]$ |
17.12.10.1 |
$12$ |
$x^{12} + 96 x^{11} + 3858 x^{10} + 83360 x^{9} + 1029255 x^{8} + 7037376 x^{7} + 22883390 x^{6} + 21113760 x^{5} + 9327045 x^{4} + 3594400 x^{3} + 16245408 x^{2} + 100784640 x + 265511268$ |
$17$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{6} + 17$ |
$[0]$ |
$[1]$ |
23.12.10.1 |
$12$ |
$x^{12} + 126 x^{11} + 6645 x^{10} + 188370 x^{9} + 3049890 x^{8} + 27314406 x^{7} + 115933067 x^{6} + 136574928 x^{5} + 76395945 x^{4} + 27661410 x^{3} + 68223420 x^{2} + 532411488 x + 1840721472$ |
$23$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{6} + 23$ |
$[0]$ |
$[1]$ |
29.12.10.1 |
$12$ |
$x^{12} + 144 x^{11} + 8652 x^{10} + 277920 x^{9} + 5045820 x^{8} + 49440384 x^{7} + 211217114 x^{6} + 98884944 x^{5} + 20432100 x^{4} + 10157760 x^{3} + 142459992 x^{2} + 1361530944 x + 5427130041$ |
$29$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 24 t + 2$ |
$x^{6} + 29$ |
$[0]$ |
$[1]$ |
41.12.10.1 |
$12$ |
$x^{12} + 228 x^{11} + 21696 x^{10} + 1104280 x^{9} + 31797420 x^{8} + 495247008 x^{7} + 3390943826 x^{6} + 2971491396 x^{5} + 1145587800 x^{4} + 282958640 x^{3} + 1289207496 x^{2} + 19090351536 x + 120389943729$ |
$41$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 38 t + 6$ |
$x^{6} + 41$ |
$[0]$ |
$[1]$ |
47.12.10.1 |
$12$ |
$x^{12} + 270 x^{11} + 30405 x^{10} + 1829250 x^{9} + 62117250 x^{8} + 1134573750 x^{7} + 8923418219 x^{6} + 5672881440 x^{5} + 1554351825 x^{4} + 313679250 x^{3} + 2881426500 x^{2} + 51396930000 x + 384516523584$ |
$47$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 45 t + 5$ |
$x^{6} + 47$ |
$[0]$ |
$[1]$ |
53.12.10.1 |
$12$ |
$x^{12} + 294 x^{11} + 36027 x^{10} + 2355920 x^{9} + 86760195 x^{8} + 1708981134 x^{7} + 14188039887 x^{6} + 3417977850 x^{5} + 348946395 x^{4} + 143243660 x^{3} + 4568329227 x^{2} + 89453326410 x + 729926391350$ |
$53$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 49 t + 2$ |
$x^{6} + 53$ |
$[0]$ |
$[1]$ |
59.12.10.1 |
$12$ |
$x^{12} + 348 x^{11} + 50472 x^{10} + 3905720 x^{9} + 170151180 x^{8} + 3961567968 x^{7} + 38748893622 x^{6} + 7923156468 x^{5} + 683578320 x^{4} + 261067280 x^{3} + 9992096472 x^{2} + 231660021168 x + 2238047928665$ |
$59$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 58 t + 2$ |
$x^{6} + 59$ |
$[0]$ |
$[1]$ |
71.12.10.1 |
$12$ |
$x^{12} + 414 x^{11} + 71457 x^{10} + 6584670 x^{9} + 342007170 x^{8} + 9522364734 x^{7} + 112699261503 x^{6} + 66656582532 x^{5} + 16763406885 x^{4} + 2722967010 x^{3} + 24170183472 x^{2} + 661393445112 x + 7594745369584$ |
$71$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 69 t + 7$ |
$x^{6} + 71$ |
$[0]$ |
$[1]$ |
83.12.10.1 |
$12$ |
$x^{12} + 492 x^{11} + 100872 x^{10} + 11032280 x^{9} + 678989580 x^{8} + 22310574432 x^{7} + 306721822950 x^{6} + 44621189700 x^{5} + 2724324720 x^{4} + 1002712400 x^{3} + 56223811992 x^{2} + 1843539438960 x + 25187542497833$ |
$83$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 82 t + 2$ |
$x^{6} + 83$ |
$[0]$ |
$[1]$ |
89.12.10.1 |
$12$ |
$x^{12} + 492 x^{11} + 100878 x^{10} + 11034740 x^{9} + 679393095 x^{8} + 22343681112 x^{7} + 308081214422 x^{6} + 67031087124 x^{5} + 6123506385 x^{4} + 1278059380 x^{3} + 60258731628 x^{2} + 1975336395024 x + 26984212327944$ |
$89$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 82 t + 3$ |
$x^{6} + 89$ |
$[0]$ |
$[1]$ |
101.12.10.1 |
$12$ |
$x^{12} + 582 x^{11} + 141147 x^{10} + 18259280 x^{9} + 1329068355 x^{8} + 51633585582 x^{7} + 838287149391 x^{6} + 103267229946 x^{5} + 5330521995 x^{4} + 1988498060 x^{3} + 134010094107 x^{2} + 5198398591626 x + 84022909229030$ |
$101$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 97 t + 2$ |
$x^{6} + 101$ |
$[0]$ |
$[1]$ |
107.12.10.1 |
$12$ |
$x^{12} + 618 x^{11} + 159147 x^{10} + 21860720 x^{9} + 1689536355 x^{8} + 69687596418 x^{7} + 1200809169003 x^{6} + 139375258962 x^{5} + 6775166445 x^{4} + 2511999020 x^{3} + 180510503637 x^{2} + 7435525591962 x + 127619121273068$ |
$107$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 103 t + 2$ |
$x^{6} + 107$ |
$[0]$ |
$[1]$ |
113.12.10.1 |
$12$ |
$x^{12} + 606 x^{11} + 153033 x^{10} + 20615110 x^{9} + 1562742330 x^{8} + 63246111726 x^{7} + 1070893850267 x^{6} + 189738403656 x^{5} + 14081961495 x^{4} + 2883033890 x^{3} + 176187317538 x^{2} + 7115373207276 x + 119740211539428$ |
$113$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 101 t + 3$ |
$x^{6} + 113$ |
$[0]$ |
$[1]$ |
131.12.10.1 |
$12$ |
$x^{12} + 762 x^{11} + 241947 x^{10} + 40975280 x^{9} + 3904105155 x^{8} + 198476052882 x^{7} + 4211487400011 x^{6} + 396952205586 x^{5} + 15648106245 x^{4} + 5692569260 x^{3} + 510934558557 x^{2} + 25952060084346 x + 549250480528100$ |
$131$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 127 t + 2$ |
$x^{6} + 131$ |
$[0]$ |
$[1]$ |
137.12.10.1 |
$12$ |
$x^{12} + 786 x^{11} + 257433 x^{10} + 44973610 x^{9} + 4420587930 x^{8} + 231881665026 x^{7} + 5080432038395 x^{6} + 695645102760 x^{5} + 39820544895 x^{4} + 7370826350 x^{3} + 604795036458 x^{2} + 31684626567780 x + 691660054409028$ |
$137$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 131 t + 3$ |
$x^{6} + 137$ |
$[0]$ |
$[1]$ |
149.12.10.1 |
$12$ |
$x^{12} + 870 x^{11} + 315387 x^{10} + 60981200 x^{9} + 6633282435 x^{8} + 384949913550 x^{7} + 9320644997583 x^{6} + 769899956730 x^{5} + 26580111675 x^{4} + 9570159500 x^{3} + 987612283947 x^{2} + 57275770431690 x + 1384032770483606$ |
$149$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 145 t + 2$ |
$x^{6} + 149$ |
$[0]$ |
$[1]$ |
167.12.10.1 |
$12$ |
$x^{12} + 996 x^{11} + 413370 x^{10} + 91510820 x^{9} + 11398264215 x^{8} + 757668341256 x^{7} + 21038145869850 x^{6} + 3788341872612 x^{5} + 285025608105 x^{4} + 26708684540 x^{3} + 1901007431580 x^{2} + 126186836966352 x + 3490535486974976$ |
$167$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 166 t + 5$ |
$x^{6} + 167$ |
$[0]$ |
$[1]$ |
173.12.10.1 |
$12$ |
$x^{12} + 1014 x^{11} + 428427 x^{10} + 96546320 x^{9} + 12239388195 x^{8} + 827730208734 x^{7} + 23347039248207 x^{6} + 1655460592890 x^{5} + 49031658195 x^{4} + 17469621260 x^{3} + 2116235170227 x^{2} + 143047015802730 x + 4028875447117550$ |
$173$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 169 t + 2$ |
$x^{6} + 173$ |
$[0]$ |
$[1]$ |
179.12.10.1 |
$12$ |
$x^{12} + 1032 x^{11} + 443772 x^{10} + 101779280 x^{9} + 13131745980 x^{8} + 903830528832 x^{7} + 25944826482822 x^{6} + 1807661242392 x^{5} + 52606406220 x^{4} + 19027183520 x^{3} + 2349318712872 x^{2} + 161621711204832 x + 4632842478742265$ |
$179$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 172 t + 2$ |
$x^{6} + 179$ |
$[0]$ |
$[1]$ |
191.12.10.1 |
$12$ |
$x^{12} + 1140 x^{11} + 541614 x^{10} + 137288300 x^{9} + 19589309415 x^{8} + 1493482775400 x^{7} + 47789883726562 x^{6} + 28376172950340 x^{5} + 7071844016445 x^{4} + 967820459100 x^{3} + 3796421982624 x^{2} + 283017421843560 x + 8957409623102124$ |
$191$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 190 t + 19$ |
$x^{6} + 191$ |
$[0]$ |
$[1]$ |
197.12.10.1 |
$12$ |
$x^{12} + 1152 x^{11} + 552972 x^{10} + 141569280 x^{9} + 20388741180 x^{8} + 1566364972032 x^{7} + 50178049081898 x^{6} + 3132730171008 x^{5} + 81663886020 x^{4} + 29014894080 x^{3} + 4014847941912 x^{2} + 308322913079808 x + 9865797905533833$ |
$197$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 192 t + 2$ |
$x^{6} + 197$ |
$[0]$ |
$[1]$ |