Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Slope content |
17.12.0.1 |
$12$ |
x12 + 3x2 - 2x + 5 |
$17$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]^{12}$ |
17.12.6.1 |
$12$ |
x12 + 117912x6 - 1419857x2 + 3475809936 |
$17$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]_{2}^{6}$ |
17.12.6.2 |
$12$ |
x12 - 1419857x2 + 289650828 |
$17$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]_{2}^{6}$ |
17.12.8.1 |
$12$ |
x12 - 51x9 + 867x6 - 4913x3 + 111166451 |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]_{3}^{4}$ |
17.12.8.2 |
$12$ |
x12 - 4913x3 + 918731 |
$17$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]_{3}^{12}$ |
17.12.9.1 |
$12$ |
x12 - 34x8 - 10115x4 - 397953 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]_{4}^{3}$ |
17.12.9.2 |
$12$ |
x12 - 34x8 + 289x4 - 44217 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]_{4}^{3}$ |
17.12.9.3 |
$12$ |
x12 - 289x4 + 14739 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]_{4}^{3}$ |
17.12.9.4 |
$12$ |
x12 + 153x8 + 7514x4 + 132651 |
$17$ |
$4$ |
$3$ |
$9$ |
$C_{12}$ (as 12T1) |
$3$ |
$4$ |
$[\ ]_{4}^{3}$ |
17.12.10.1 |
$12$ |
x12 - 170x6 + 210681 |
$17$ |
$6$ |
$2$ |
$10$ |
$D_6$ (as 12T3) |
$2$ |
$6$ |
$[\ ]_{6}^{2}$ |
17.12.10.2 |
$12$ |
x12 + 85x6 + 2601 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$6$ |
$[\ ]_{6}^{6}$ |
17.12.10.3 |
$12$ |
x12 + 136x6 + 7803 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$6$ |
$[\ ]_{6}^{2}$ |
17.12.10.4 |
$12$ |
x12 - 17x6 + 867 |
$17$ |
$6$ |
$2$ |
$10$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$6$ |
$[\ ]_{6}^{6}$ |
17.12.11.1 |
$12$ |
x12 - 17 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]_{12}^{2}$ |
17.12.11.2 |
$12$ |
x12 - 153 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]_{12}^{2}$ |
17.12.11.3 |
$12$ |
x12 + 51 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]_{12}^{2}$ |
17.12.11.4 |
$12$ |
x12 + 459 |
$17$ |
$12$ |
$1$ |
$11$ |
$S_3 \times C_4$ (as 12T11) |
$2$ |
$12$ |
$[\ ]_{12}^{2}$ |