Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
11.12.0.1 |
$12$ |
x12 + x8 + x7 + 4x6 + 2x5 + 5x4 + 5x3 + 6x2 + 5x + 2 |
$11$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$[0]$ |
$[]$ |
11.12.6.1 |
$12$ |
x12 + 72x10 + 8x9 + 2034x8 + 38x7 + 27996x6 - 6312x5 + 196025x4 - 84710x3 + 695581x2 - 235284x + 1080083 |
$11$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
11.12.6.2 |
$12$ |
x12 + 363x8 - 5324x6 + 87846x4 - 1127357x2 + 3543122 |
$11$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
11.12.8.1 |
$12$ |
x12 + 24x10 + 74x9 + 198x8 + 480x7 - 346x6 + 5208x5 - 3276x4 - 856x3 + 53628x2 - 74328x + 152743 |
$11$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$[0]$ |
$[1]$ |
11.12.8.2 |
$12$ |
x12 - 176x9 + 8228x6 + 90508x3 + 58564 |
$11$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$[0]$ |
$[1]$ |
11.12.9.1 |
$12$ |
x12 + 8x10 + 36x9 + 57x8 + 216x7 + 342x6 - 4320x5 + 2675x4 + 2412x3 + 26122x2 + 17316x + 16164 |
$11$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[0]$ |
$[2]$ |
11.12.9.2 |
$12$ |
x12 + 242x4 - 11979 |
$11$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[0]$ |
$[2]$ |
11.12.10.1 |
$12$ |
x12 + 42x11 + 747x10 + 7280x9 + 41955x8 + 143682x7 + 279531x6 + 287826x5 + 175245x4 + 124460x3 + 344757x2 + 893466x + 996620 |
$11$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
11.12.10.2 |
$12$ |
x12 - 198x6 - 10043 |
$11$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$[0]$ |
$[1]$ |
11.12.10.3 |
$12$ |
x12 - 165x6 - 4356 |
$11$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
11.12.10.4 |
$12$ |
x12 - 704x6 - 121 |
$11$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$[0]$ |
$[1]$ |
11.12.11.1 |
$12$ |
x12 + 11 |
$11$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
11.12.11.2 |
$12$ |
x12 + 22 |
$11$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |