| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
| 19.12.0.1 |
$12$ |
x12 + 3x7 + 2x6 + 18x5 + 2x4 + 9x3 + 16x2 + 7x + 2 |
$19$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$[0]$ |
$[]$ |
| 19.12.6.1 |
$12$ |
x12 + 114x10 + 34x9 + 5449x8 + 12x7 + 134889x6 - 75118x5 + 1847901x4 - 1865072x3 + 14269503x2 - 12672520x + 53461691 |
$19$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
| 19.12.6.2 |
$12$ |
x12 - 116603x6 + 2215457x4 - 14856594x2 + 94091762 |
$19$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[0]$ |
$[1]$ |
| 19.12.8.1 |
$12$ |
x12 + 386x10 + 109x9 + 55308x8 + 21792x7 + 3500499x6 + 2034936x5 + 84821873x4 + 99877907x3 + 174885148x2 + 920938017x + 335157671 |
$19$ |
$3$ |
$4$ |
$8$ |
$C_{12}$ (as 12T1) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$[0]$ |
$[1]$ |
| 19.12.8.2 |
$12$ |
x12 - 76x9 + 2888x6 + 775067x3 + 521284 |
$19$ |
$3$ |
$4$ |
$8$ |
$C_{12}$ (as 12T1) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$[0]$ |
$[1]$ |
| 19.12.8.3 |
$12$ |
x12 + 722x6 - 75449x3 + 260642 |
$19$ |
$3$ |
$4$ |
$8$ |
$C_{12}$ (as 12T1) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$[0]$ |
$[1]$ |
| 19.12.9.1 |
$12$ |
x12 + 16x10 + 68x9 + 153x8 + 816x7 + 1382x6 - 12240x5 + 17643x4 + 18836x3 + 180010x2 + 131580x + 194652 |
$19$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[0]$ |
$[2]$ |
| 19.12.9.2 |
$12$ |
x12 + 1444x4 - 116603 |
$19$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[0]$ |
$[2]$ |
| 19.12.10.1 |
$12$ |
x12 + 108x11 + 4872x10 + 117720x9 + 1613580x8 + 12041568x7 + 40427622x6 + 24085188x5 + 6545520x4 + 3116880x3 + 29259672x2 + 208806768x + 622519465 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.10.2 |
$12$ |
x12 + 304x6 - 5415 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.10.3 |
$12$ |
x12 - 5396x6 - 21660 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.10.4 |
$12$ |
x12 - 342x6 + 722 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_{12}$ (as 12T1) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.10.5 |
$12$ |
x12 - 5510x6 - 1650131 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_{12}$ (as 12T1) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.10.6 |
$12$ |
x12 - 5928x6 - 454860 |
$19$ |
$6$ |
$2$ |
$10$ |
$C_{12}$ (as 12T1) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[0]$ |
$[1]$ |
| 19.12.11.1 |
$12$ |
x12 + 76 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
| 19.12.11.2 |
$12$ |
x12 + 19 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
| 19.12.11.3 |
$12$ |
x12 + 95 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
| 19.12.11.4 |
$12$ |
x12 + 152 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
| 19.12.11.5 |
$12$ |
x12 + 38 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
| 19.12.11.6 |
$12$ |
x12 + 190 |
$19$ |
$12$ |
$1$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[0]$ |
$[2]$ |
