| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.0.1 |
$12$ |
$x^{12} + x^{6} + x^{5} + x^{4} + x^{2} + 2$ |
$3$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{6} + t^{5} + t^{4} + t^{2} + 2$ |
$x - 3$ |
$[0]$ |
$[]$ |
| 3.12.6.1 |
$12$ |
$x^{12} + 18 x^{8} + 81 x^{4} - 486 x^{2} + 1458$ |
$3$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
| 3.12.16.14 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 768 x^{9} - 432 x^{8} - 10368 x^{7} - 18414 x^{6} + 27864 x^{5} + 83592 x^{4} + 10800 x^{3} + 64800 x^{2} + 901125$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 9 t^{3} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.25 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 804 x^{9} + 216 x^{8} - 6480 x^{7} - 11610 x^{6} + 16200 x^{5} + 48600 x^{4} + 33156 x^{3} + 198936 x^{2} + 190593$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 18 t^{3} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.40 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 840 x^{9} + 864 x^{8} - 2592 x^{7} - 4482 x^{6} + 8424 x^{5} + 25272 x^{4} + 4968 x^{3} + 29808 x^{2} + 139077$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 18 t^{3} + 9 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.18.61 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 42 x^{9} + 54 x^{8} + 18 x^{7} + 21 x^{6} + 72 x^{5} + 108 x^{4} + 36 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_{12}$ (as 12T1) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.74 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 42 x^{9} + 54 x^{8} + 18 x^{7} - 33 x^{6} - 252 x^{5} - 126 x^{3} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_{12}$ (as 12T1) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.88 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 42 x^{9} + 54 x^{8} + 18 x^{7} + 21 x^{6} + 72 x^{5} + 54 x^{4} + 36 x^{3} + 45$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_{12}$ (as 12T1) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 3 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
