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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.12.1 $x^{12} - 36 x^{10} + 12 x^{9} + 540 x^{8} - 324 x^{7} - 3402 x^{6} + 3240 x^{5} + 8424 x^{4} - 10260 x^{3} + 4860 x^{2} - 972 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 3 t^{2}\right) x + 3$
3.12.12.10 $x^{12} - 24 x^{11} + 306 x^{10} - 2004 x^{9} + 7236 x^{8} - 4374 x^{7} - 1458 x^{6} + 5832 x^{5} - 1836 x^{3} + 324 x^{2} + 486 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t^{2}\right) x^{2} + \left(3 t + 6\right) x + 3$
3.12.12.13 $x^{12} - 36 x^{11} + 324 x^{10} + 588 x^{9} + 9414 x^{8} + 56376 x^{7} + 114642 x^{6} + 92448 x^{5} + 23409 x^{4} + 2376 x^{3} + 3078 x^{2} - 972 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 6 t + 3\right) x + 3$
3.12.12.14 $x^{12} + 54 x^{10} - 240 x^{9} - 1935 x^{8} + 7236 x^{7} + 45198 x^{6} + 60156 x^{5} + 16686 x^{4} - 13824 x^{3} + 5184 x^{2} - 972 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + \left(6 t^{3} + 6 t^{2} + 6 t\right) x + 3$
3.12.12.15 $x^{12} - 18 x^{11} + 186 x^{10} - 798 x^{9} + 2817 x^{8} + 30456 x^{7} + 55404 x^{6} + 28404 x^{5} - 2511 x^{4} + 918 x^{3} + 2754 x^{2} - 810 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t + 3\right) x + 3$
3.12.12.2 $x^{12} - 48 x^{11} + 606 x^{10} + 2856 x^{9} + 29529 x^{8} + 112428 x^{7} + 183222 x^{6} + 125172 x^{5} + 19926 x^{4} + 3024 x^{3} + 9072 x^{2} - 1620 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + \left(6 t^{3} + 6 t\right) x + 3$
3.12.12.20 $x^{12} + 30 x^{10} + 228 x^{9} + 1872 x^{8} + 5778 x^{7} + 15336 x^{6} + 18036 x^{5} + 12879 x^{4} + 7074 x^{3} + 3240 x^{2} + 810 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 6 t^{2}\right) x^{2} + \left(6 t^{2} + 3 t + 3\right) x + 3$
3.12.12.21 $x^{12} - 6 x^{11} + 60 x^{10} - 114 x^{9} + 2286 x^{8} + 33750 x^{7} + 101790 x^{6} + 91152 x^{5} + 24867 x^{4} + 6102 x^{3} + 5832 x^{2} - 1296 x + 81$ $3$ $3$ $4$ $12$ $C_3^2:F_9$ (as 12T173) $[3/2]$ $[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{3} + 6 t + 3\right) x + 3$
3.12.16.18 $x^{12} - 474 x^{9} + 5292 x^{8} - 972 x^{7} + 66960 x^{6} + 9396 x^{5} + 274104 x^{4} + 15660 x^{3} + 432540 x^{2} + 234090$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + 9 t^{3} + 9 t + 12$
3.12.16.2 $x^{12} - 54 x^{10} - 258 x^{9} + 2403 x^{8} - 1134 x^{7} + 27594 x^{6} - 6480 x^{5} + 134136 x^{4} - 26136 x^{3} + 351864 x^{2} + 490698$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$
3.12.16.26 $x^{12} - 18 x^{11} + 144 x^{10} - 690 x^{9} + 2970 x^{8} - 6588 x^{7} + 33588 x^{6} - 23004 x^{5} + 185976 x^{4} - 26136 x^{3} + 486972 x^{2} + 490698$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$
3.12.16.29 $x^{12} - 48 x^{11} + 666 x^{10} + 1146 x^{9} + 27891 x^{8} - 12690 x^{7} + 138726 x^{6} - 14580 x^{5} - 61560 x^{4} + 32670 x^{3} - 554850 x^{2} + 463725$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + 18 t^{2} + 9 t + 3$
3.12.16.31 $x^{12} + 30 x^{11} + 360 x^{10} + 2226 x^{9} + 7641 x^{8} - 4320 x^{7} - 24408 x^{6} - 21060 x^{5} - 255312 x^{4} - 22248 x^{3} + 454248 x^{2} + 2375892$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{2} + 3 t + 3\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 12$
3.12.16.34 $x^{12} - 60 x^{11} + 1152 x^{10} - 4308 x^{9} + 33480 x^{8} + 432 x^{7} + 96120 x^{6} - 4536 x^{5} + 95904 x^{4} + 1080 x^{3} + 12960 x^{2} + 8100$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 12$
3.12.16.7 $x^{12} - 18 x^{11} + 72 x^{10} + 444 x^{9} + 2619 x^{8} + 4806 x^{7} + 29862 x^{6} + 15228 x^{5} + 140616 x^{4} + 15660 x^{3} + 296460 x^{2} + 234090$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 3 t + 3\right) x^{2} + 9 t^{3} + 9 t + 12$
3.12.16.8 $x^{12} + 24 x^{11} + 252 x^{10} + 1146 x^{9} + 2808 x^{8} + 7020 x^{7} + 14472 x^{6} + 16200 x^{5} + 42120 x^{4} + 13230 x^{3} + 64800 x^{2} + 40905$ $3$ $3$ $4$ $16$ $C_3^2:F_9$ (as 12T173) $[2]$ $[2, 2, 2, 2]^{8}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 9 t + 21$
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