| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 17.12.0.1 |
$12$ |
$x^{12} + x^{8} + 4 x^{7} + 14 x^{6} + 14 x^{5} + 13 x^{4} + 6 x^{3} + 14 x^{2} + 9 x + 3$ |
$17$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{8} + 4 t^{7} + 14 t^{6} + 14 t^{5} + 13 t^{4} + 6 t^{3} + 14 t^{2} + 9 t + 3$ |
$x - 17$ |
$[0]$ |
$[]$ |
| 17.12.6.1 |
$12$ |
$x^{12} + 918 x^{11} + 351241 x^{10} + 71712630 x^{9} + 8244584136 x^{8} + 506874732756 x^{7} + 13125344775560 x^{6} + 9625198256031 x^{5} + 28457943732288 x^{4} + 16844354225613 x^{3} + 132306217741765 x^{2} + 68598705820311 x + 44162739951115$ |
$17$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 17.12.6.2 |
$12$ |
$x^{12} + 578 x^{8} + 835210 x^{4} - 4259571 x^{2} + 72412707$ |
$17$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.12.8.1 |
$12$ |
$x^{12} + 225 x^{10} + 98 x^{9} + 17904 x^{8} + 10824 x^{7} + 611647 x^{6} + 498390 x^{5} + 8494833 x^{4} + 11764900 x^{3} + 38205036 x^{2} + 73669974 x + 36476587$ |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{3} + 51 x + 17$ |
$[0]$ |
$[1]$ |
| 17.12.8.2 |
$12$ |
$x^{12} + 2023 x^{6} - 49130 x^{3} + 250563$ |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{3} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.12.9.1 |
$12$ |
$x^{12} + 4 x^{10} + 56 x^{9} + 57 x^{8} + 168 x^{7} + 1044 x^{6} - 11256 x^{5} + 3356 x^{4} + 10080 x^{3} + 97736 x^{2} + 58576 x + 57252$ |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$t^{3} + t + 14$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
| 17.12.9.2 |
$12$ |
$x^{12} - 34 x^{8} + 289 x^{4} + 962948$ |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$t^{3} + t + 14$ |
$x^{4} + 17 t^{2}$ |
$[0]$ |
$[1]$ |
| 17.12.9.3 |
$12$ |
$x^{12} + 289 x^{4} - 68782$ |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$t^{3} + t + 14$ |
$x^{4} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.12.9.4 |
$12$ |
$x^{12} + 153 x^{8} + 81787 x^{4} - 277825237$ |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{3}$ |
$t^{3} + t + 14$ |
$x^{4} + 272 t + 51$ |
$[0]$ |
$[1]$ |
| 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) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{6} + 17$ |
$[0]$ |
$[1]$ |
| 17.12.10.2 |
$12$ |
$x^{12} - 3060 x^{6} - 197676$ |
$17$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 16 t + 3$ |
$x^{6} + 204 t + 102$ |
$[0]$ |
$[1]$ |
| 17.12.10.3 |
$12$ |
$x^{12} - 3604 x^{6} - 719321$ |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 16 t + 3$ |
$x^{6} + 255 t + 238$ |
$[0]$ |
$[1]$ |
| 17.12.10.4 |
$12$ |
$x^{12} + 238 x^{6} - 3468$ |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 16 t + 3$ |
$x^{6} + 17 t + 255$ |
$[0]$ |
$[1]$ |
| 17.12.11.1 |
$12$ |
$x^{12} + 17$ |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 14$ |
$x^{12} + 17$ |
$[0]$ |
$[2]$ |
| 17.12.11.2 |
$12$ |
$x^{12} + 34$ |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 14$ |
$x^{12} + 34$ |
$[0]$ |
$[2]$ |
| 17.12.11.3 |
$12$ |
$x^{12} + 51$ |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 14$ |
$x^{12} + 51$ |
$[0]$ |
$[2]$ |
| 17.12.11.4 |
$12$ |
$x^{12} + 102$ |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 14$ |
$x^{12} + 102$ |
$[0]$ |
$[2]$ |
