| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 23.12.0.1 |
$12$ |
$x^{12} + 21 x^{7} + 21 x^{6} + 15 x^{5} + 14 x^{4} + 12 x^{3} + 18 x^{2} + 12 x + 5$ |
$23$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + 21 t^{7} + 21 t^{6} + 15 t^{5} + 14 t^{4} + 12 t^{3} + 18 t^{2} + 12 t + 5$ |
$x - 23$ |
$[0]$ |
$[]$ |
| 23.12.6.1 |
$12$ |
$x^{12} + 140 x^{10} + 18 x^{9} + 8092 x^{8} + 20 x^{7} + 244001 x^{6} - 56140 x^{5} + 4059563 x^{4} - 1721304 x^{3} + 36312468 x^{2} - 14694000 x + 141161628$ |
$23$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + t^{4} + 9 t^{3} + 9 t^{2} + t + 5$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
| 23.12.6.2 |
$12$ |
$x^{12} + 529 x^{8} - 109503 x^{6} + 2518569 x^{4} - 6436343 x^{2} + 740179445$ |
$23$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + t^{4} + 9 t^{3} + 9 t^{2} + t + 5$ |
$x^{2} + 23 t$ |
$[0]$ |
$[1]$ |
| 23.12.8.1 |
$12$ |
$x^{12} + 9 x^{10} + 149 x^{9} + 42 x^{8} + 342 x^{7} - 3492 x^{6} - 3195 x^{5} - 6891 x^{4} - 80901 x^{3} + 124182 x^{2} - 232623 x + 1674962$ |
$23$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{3} + 23$ |
$[0]$ |
$[1]$ |
| 23.12.8.2 |
$12$ |
$x^{12} - 138 x^{9} + 10051 x^{6} + 4027277 x^{3} + 6996025$ |
$23$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{3} + 23 t^{2}$ |
$[0]$ |
$[1]$ |
| 23.12.9.1 |
$12$ |
$x^{12} + 8 x^{10} + 72 x^{9} + 93 x^{8} + 432 x^{7} + 1608 x^{6} - 19008 x^{5} + 10115 x^{4} + 20592 x^{3} + 219376 x^{2} + 154296 x + 181359$ |
$23$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 18$ |
$x^{4} + 23$ |
$[0]$ |
$[2]$ |
| 23.12.9.2 |
$12$ |
$x^{12} + 1058 x^{4} - 219006$ |
$23$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 18$ |
$x^{4} + 23 t$ |
$[0]$ |
$[2]$ |
| 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) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{6} + 23$ |
$[0]$ |
$[1]$ |
| 23.12.10.2 |
$12$ |
$x^{12} - 138 x^{6} - 217948$ |
$23$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 21 t + 5$ |
$x^{6} + 46 t + 414$ |
$[0]$ |
$[1]$ |
| 23.12.10.3 |
$12$ |
$x^{12} - 10028 x^{6} - 1807593$ |
$23$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$t^{2} + 21 t + 5$ |
$x^{6} + 506 t + 299$ |
$[0]$ |
$[1]$ |
| 23.12.10.4 |
$12$ |
$x^{12} - 483 x^{6} + 2645$ |
$23$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{2} + 21 t + 5$ |
$x^{6} + 23 t$ |
$[0]$ |
$[1]$ |
| 23.12.11.1 |
$12$ |
$x^{12} + 23$ |
$23$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 18$ |
$x^{12} + 23$ |
$[0]$ |
$[2]$ |
| 23.12.11.2 |
$12$ |
$x^{12} + 115$ |
$23$ |
$12$ |
$1$ |
$11$ |
$D_{12}$ (as 12T12) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$t + 18$ |
$x^{12} + 115$ |
$[0]$ |
$[2]$ |
