| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.0.1 |
$12$ |
$x^{12} + x^{7} + x^{6} + x^{5} + x^{3} + x + 1$ |
$2$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{7} + t^{6} + t^{5} + t^{3} + t + 1$ |
$x - 2$ |
$[0]$ |
$[]$ |
| 2.12.12.25 |
$12$ |
$x^{12} + 12 x^{11} + 60 x^{10} + 160 x^{9} + 308 x^{8} + 736 x^{7} + 2272 x^{6} + 5632 x^{5} + 10608 x^{4} + 15040 x^{3} + 12224 x^{2} + 3584 x + 704$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.18.27 |
$12$ |
$x^{12} + 24 x^{11} + 300 x^{10} + 2480 x^{9} + 15084 x^{8} + 70848 x^{7} + 263968 x^{6} + 785280 x^{5} + 1858672 x^{4} + 3423104 x^{3} + 4742336 x^{2} + 4511488 x + 2639680$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 x + 8 t^{3} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.28 |
$12$ |
$x^{12} + 12 x^{11} + 128 x^{10} + 1032 x^{9} + 8068 x^{8} + 54752 x^{7} + 298816 x^{6} + 1148736 x^{5} + 2948656 x^{4} + 4481984 x^{3} + 2851584 x^{2} - 296320 x + 1412800$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 4 t^{5} + 12 t^{4} + 12 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.33.321 |
$12$ |
$x^{12} - 16 x^{11} + 100 x^{10} + 128 x^{9} + 1198 x^{8} - 1792 x^{7} + 3856 x^{6} + 6144 x^{5} + 1356 x^{4} + 6720 x^{3} + 19728 x^{2} + 1768$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 12 x^{2} + 16 t^{2} + 24 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.34 |
$12$ |
$x^{12} - 16 x^{11} + 100 x^{10} + 128 x^{9} + 1278 x^{8} - 2560 x^{7} + 3728 x^{6} - 3072 x^{5} + 13836 x^{4} + 4160 x^{3} + 31248 x^{2} + 18728$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 12 x^{2} + 24 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.340 |
$12$ |
$x^{12} + 76 x^{10} - 384 x^{9} - 1170 x^{8} - 512 x^{7} - 592 x^{6} + 256 x^{5} + 1484 x^{4} + 1536 x^{3} + 2992 x^{2} + 6376$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t + 4\right) x^{2} + 16 t^{2} + 8 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.344 |
$12$ |
$x^{12} + 56 x^{10} - 392 x^{9} + 226 x^{8} - 640 x^{7} - 2480 x^{6} + 3968 x^{5} + 1276 x^{4} - 384 x^{3} + 9280 x^{2} + 24224 x + 31544$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{2} x^{2} + \left(8 t + 8\right) x + 4 t^{2} + 28 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.369 |
$12$ |
$x^{12} + 76 x^{10} - 384 x^{9} - 1090 x^{8} - 896 x^{7} + 688 x^{6} + 768 x^{5} + 3980 x^{4} + 1792 x^{3} + 10160 x^{2} + 18728$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t + 4\right) x^{2} + 8 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.374 |
$12$ |
$x^{12} + 80 x^{10} - 264 x^{9} - 622 x^{8} + 448 x^{7} + 1744 x^{6} + 10176 x^{5} + 19740 x^{4} + 34304 x^{3} + 45664 x^{2} + 26400 x + 45496$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{2} + 8 t + 8\right) x^{2} + \left(8 t + 8\right) x + 28 t^{2} + 12 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.375 |
$12$ |
$x^{12} + 80 x^{10} - 264 x^{9} - 638 x^{8} + 64 x^{7} + 208 x^{6} + 3904 x^{5} + 8348 x^{4} + 10496 x^{3} + 13152 x^{2} + 7200 x + 6392$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{2} + 8 t + 8\right) x^{2} + \left(8 t + 8\right) x + 12 t^{2} + 12 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.376 |
$12$ |
$x^{12} + 56 x^{10} - 392 x^{9} + 146 x^{8} - 256 x^{7} - 3120 x^{6} + 512 x^{5} + 1788 x^{4} - 6272 x^{3} + 8768 x^{2} + 9632 x + 9848$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_{12}$ (as 12T1) |
$3$ |
$1$ |
$[3, 4]$ |
$[3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{2} x^{2} + \left(8 t + 8\right) x + 20 t^{2} + 28 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
