| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 11.12.0.1 |
$12$ |
$x^{12} + x^{8} + x^{7} + 4 x^{6} + 2 x^{5} + 5 x^{4} + 5 x^{3} + 6 x^{2} + 5 x + 2$ |
$11$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{8} + t^{7} + 4 t^{6} + 2 t^{5} + 5 t^{4} + 5 t^{3} + 6 t^{2} + 5 t + 2$ |
$x - 11$ |
$[0]$ |
$[\ ]$ |
| 11.12.6.1 |
$12$ |
$x^{12} + 72 x^{10} + 8 x^{9} + 2034 x^{8} + 38 x^{7} + 27996 x^{6} - 6312 x^{5} + 196025 x^{4} - 84710 x^{3} + 695581 x^{2} - 235284 x + 1080083$ |
$11$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 3 t^{4} + 4 t^{3} + 6 t^{2} + 7 t + 2$ |
$x^{2} + 11$ |
$[0]$ |
$[1]$ |
| 11.12.6.2 |
$12$ |
$x^{12} + 363 x^{8} - 5324 x^{6} + 87846 x^{4} - 1127357 x^{2} + 3543122$ |
$11$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 3 t^{4} + 4 t^{3} + 6 t^{2} + 7 t + 2$ |
$x^{2} + 11 t$ |
$[0]$ |
$[1]$ |
| 11.12.8.1 |
$12$ |
$x^{12} + 24 x^{10} + 74 x^{9} + 198 x^{8} + 480 x^{7} - 346 x^{6} + 5208 x^{5} - 3276 x^{4} - 856 x^{3} + 53628 x^{2} - 74328 x + 152743$ |
$11$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{3} + 11$ |
$[0]$ |
$[1]$ |
| 11.12.8.2 |
$12$ |
$x^{12} - 176 x^{9} + 8228 x^{6} + 90508 x^{3} + 58564$ |
$11$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{3} + 11 t^{2}$ |
$[0]$ |
$[1]$ |
| 11.12.9.1 |
$12$ |
$x^{12} + 8 x^{10} + 36 x^{9} + 57 x^{8} + 216 x^{7} + 342 x^{6} - 4320 x^{5} + 2675 x^{4} + 2412 x^{3} + 26122 x^{2} + 17316 x + 16164$ |
$11$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 9$ |
$x^{4} + 11$ |
$[0]$ |
$[2]$ |
| 11.12.9.2 |
$12$ |
$x^{12} + 242 x^{4} - 11979$ |
$11$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 9$ |
$x^{4} + 11 t$ |
$[0]$ |
$[2]$ |
| 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) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{6} + 11$ |
$[0]$ |
$[1]$ |
| 11.12.10.2 |
$12$ |
$x^{12} - 198 x^{6} - 10043$ |
$11$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 7 t + 2$ |
$x^{6} + 44 t + 55$ |
$[0]$ |
$[1]$ |
| 11.12.10.3 |
$12$ |
$x^{12} - 165 x^{6} - 4356$ |
$11$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 7 t + 2$ |
$x^{6} + 33 t + 33$ |
$[0]$ |
$[1]$ |
| 11.12.10.4 |
$12$ |
$x^{12} - 704 x^{6} - 121$ |
$11$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 7 t + 2$ |
$x^{6} + 110 t + 33$ |
$[0]$ |
$[1]$ |
| 11.12.11.1 |
$12$ |
$x^{12} + 11$ |
$11$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 9$ |
$x^{12} + 11$ |
$[0]$ |
$[2]$ |
| 11.12.11.2 |
$12$ |
$x^{12} + 22$ |
$11$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 9$ |
$x^{12} + 22$ |
$[0]$ |
$[2]$ |
