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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.14.8 $x^{12} + 42 x^{6} + 72 x^{5} + 36 x^{4} + 9$ $3$ $6$ $2$ $14$ $C_3\times S_3^2$ (as 12T70) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3$
3.12.18.17 $x^{12} + 12 x^{11} + 48 x^{10} + 72 x^{9} + 36 x^{8} + 60 x^{6} + 144 x^{5} + 144 x^{4} + 108 x^{3} + 225$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 9 t + 21$
3.12.18.21 $x^{12} - 6 x^{9} + 36 x^{8} + 36 x^{7} + 24 x^{6} - 18 x^{3} + 9$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{4} + 3 t x^{3} + 3$
3.12.18.23 $x^{12} + 12 x^{11} + 48 x^{10} + 72 x^{9} + 36 x^{8} + 42 x^{6} + 36 x^{5} + 36 x^{4} + 216 x^{3} + 333$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 18 t + 21$
3.12.18.28 $x^{12} + 6 x^{11} + 24 x^{10} + 12 x^{9} + 27 x^{8} - 18 x^{7} + 51 x^{6} + 18 x^{5} + 18 x^{4} - 18 x^{3} + 9$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{5} + 3 x^{4} + \left(6 t + 3\right) x^{3} + 3$
3.12.18.41 $x^{12} + 6 x^{11} + 9 x^{10} + 6 x^{9} + 54 x^{8} - 3 x^{6} - 36 x^{5} + 108 x^{4} - 36 x^{3} + 117$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{5} + \left(6 t + 6\right) x^{4} + 3 x^{3} + 9 t + 3$
3.12.18.45 $x^{12} - 12 x^{11} + 84 x^{10} - 72 x^{9} + 36 x^{8} + 6 x^{6} - 36 x^{5} + 36 x^{4} + 9$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + 6 x^{4} + 3$
3.12.18.48 $x^{12} - 12 x^{11} + 72 x^{10} + 36 x^{9} + 81 x^{8} + 36 x^{7} + 42 x^{6} - 36 x^{5} + 9$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + \left(3 t + 3\right) x^{4} + \left(6 t + 6\right) x^{3} + 3$
3.12.18.57 $x^{12} - 12 x^{11} + 72 x^{10} + 66 x^{9} + 108 x^{8} + 36 x^{7} + 60 x^{6} - 252 x^{5} - 126 x^{3} + 441$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + \left(6 t + 6\right) x^{4} + 3 t x^{3} + 21$
3.12.18.58 $x^{12} + 12 x^{11} + 42 x^{10} + 30 x^{9} - 27 x^{8} - 18 x^{7} + 87 x^{6} + 252 x^{5} + 126 x^{4} - 126 x^{3} + 441$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + 3 x^{4} + \left(6 t + 3\right) x^{3} + 21$
3.12.18.60 $x^{12} + 12 x^{11} + 36 x^{10} - 12 x^{9} - 36 x^{8} + 72 x^{7} + 78 x^{6} + 36 x^{5} + 108 x^{4} + 72 x^{3} + 90$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + \left(6 t + 6\right) x^{4} + 6 t x^{3} + 9 t + 12$
3.12.18.9 $x^{12} - 6 x^{11} + 45 x^{10} + 72 x^{9} + 36 x^{8} - 12 x^{6} + 144 x^{5} + 108 x^{4} + 117$ $3$ $6$ $2$ $18$ $C_3\times S_3^2$ (as 12T70) $[2]$ $[3/2, 2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + \left(6 t + 6\right) x^{4} + 9 t + 3$
3.12.22.28 $x^{12} + 24 x^{9} - 18 x^{8} + 36 x^{7} + 150 x^{6} - 216 x^{5} + 837 x^{4} - 252 x^{3} + 270 x^{2} + 108 x + 9$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 12 x^{3} + \left(18 t + 9\right) x^{2} + 18 x + 3$
3.12.22.30 $x^{12} - 18 x^{9} + 18 x^{8} - 18 x^{7} + 645 x^{6} + 270 x^{5} + 756 x^{4} + 540 x^{3} + 216 x^{2} + 270 x + 117$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(24 t + 15\right) x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 9 t + 3$
3.12.22.31 $x^{12} - 24 x^{9} - 18 x^{7} + 375 x^{6} + 270 x^{5} + 837 x^{4} + 522 x^{3} + 567 x^{2} + 270 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(15 t + 3\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(18 t + 9\right) x + 9 t + 12$
3.12.22.33 $x^{12} + 24 x^{9} + 36 x^{8} + 132 x^{6} + 432 x^{5} + 324 x^{4} - 144 x^{3} - 216 x^{2} + 117$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 12 x^{3} + 18 x^{2} + 9 t + 3$
3.12.22.36 $x^{12} - 18 x^{9} - 18 x^{8} + 492 x^{6} + 918 x^{5} + 783 x^{4} + 1350 x^{3} + 999 x^{2} + 324 x + 549$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(21 t + 12\right) x^{3} + \left(18 t + 9\right) x^{2} + \left(9 t + 9\right) x + 18 t + 3$
3.12.22.43 $x^{12} + 18 x^{9} + 18 x^{8} - 18 x^{7} + 312 x^{6} + 432 x^{5} + 270 x^{4} + 324 x^{3} + 378 x^{2} + 108 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(15 t + 24\right) x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 9 t + 12$
3.12.22.45 $x^{12} + 6 x^{9} - 18 x^{7} + 96 x^{6} + 108 x^{4} + 342 x^{3} + 162 x^{2} + 270 x + 333$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(9 t + 12\right) x^{3} + 9 t x + 18 t + 21$
3.12.22.50 $x^{12} - 24 x^{9} + 36 x^{8} - 18 x^{7} + 375 x^{6} - 432 x^{5} + 810 x^{4} - 126 x^{3} + 270 x^{2} + 108 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(15 t + 3\right) x^{3} + 18 x^{2} + 9 t x + 9 t + 12$
3.12.22.51 $x^{12} - 24 x^{9} - 36 x^{8} - 18 x^{7} + 726 x^{6} + 1296 x^{5} + 1296 x^{4} + 576 x^{3} + 54 x^{2} - 54 x + 9$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(24 t + 12\right) x^{3} + 18 t x^{2} + 9 t x + 3$
3.12.22.53 $x^{12} + 12 x^{9} - 36 x^{8} + 366 x^{6} + 432 x^{5} + 1296 x^{4} + 1008 x^{3} + 540 x^{2} + 324 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(18 t + 24\right) x^{3} + 18 t x^{2} + \left(18 t + 18\right) x + 9 t + 12$
3.12.22.56 $x^{12} - 12 x^{9} - 18 x^{7} + 600 x^{6} + 864 x^{5} + 1296 x^{4} + 1152 x^{3} + 729 x^{2} + 432 x + 117$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(24 t + 18\right) x^{3} + \left(18 t + 18\right) x^{2} + \left(18 t + 9\right) x + 9 t + 3$
3.12.22.58 $x^{12} - 6 x^{9} - 18 x^{8} + 456 x^{6} + 432 x^{5} + 918 x^{4} + 684 x^{3} + 432 x^{2} + 324 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(21 t + 18\right) x^{3} + 9 t x^{2} + \left(18 t + 18\right) x + 9 t + 12$
3.12.22.59 $x^{12} - 12 x^{9} - 18 x^{8} + 249 x^{6} + 378 x^{5} + 432 x^{4} + 774 x^{3} + 513 x^{2} + 324 x + 360$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(15 t + 9\right) x^{3} + 9 t x^{2} + \left(9 t + 9\right) x + 18 t + 12$
3.12.22.62 $x^{12} + 6 x^{9} - 18 x^{7} + 33 x^{6} + 27 x^{4} + 234 x^{3} + 162 x^{2} - 216 x + 144$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{3} + \left(9 t + 9\right) x^{2} + 9 t x + 12$
3.12.22.69 $x^{12} - 48 x^{9} + 36 x^{8} - 18 x^{7} + 1176 x^{6} - 864 x^{5} + 1188 x^{4} - 468 x^{3} + 594 x^{2} - 54 x + 225$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 24 t x^{3} + 18 x^{2} + 9 t x + 9 t + 21$
3.12.22.71 $x^{12} + 24 x^{9} + 150 x^{6} + 72 x^{3} + 324 x^{2} + 324 x + 90$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 12 x^{3} + \left(18 t + 18\right) x + 9 t + 12$
3.12.22.72 $x^{12} + 6 x^{9} + 18 x^{8} + 36 x^{7} + 51 x^{6} + 54 x^{5} + 270 x^{4} + 450 x^{3} + 702 x^{2} + 756 x + 441$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{3} + \left(9 t + 18\right) x^{2} + 18 x + 21$
3.12.22.73 $x^{12} - 18 x^{9} + 36 x^{7} + 294 x^{6} + 270 x^{5} - 243 x^{4} + 648 x^{3} + 648 x^{2} - 216 x + 360$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(15 t + 6\right) x^{3} + \left(9 t + 9\right) x^{2} + 18 x + 18 t + 12$
3.12.22.74 $x^{12} + 18 x^{8} + 168 x^{6} + 513 x^{4} + 216 x^{3} + 540 x^{2} + 324 x + 225$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(12 t + 12\right) x^{3} + 9 x^{2} + \left(18 t + 18\right) x + 9 t + 21$
3.12.22.76 $x^{12} + 30 x^{9} - 36 x^{7} + 294 x^{6} - 216 x^{4} + 144 x^{3} + 648 x^{2} + 864 x + 360$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(9 t + 24\right) x^{3} + 18 t x + 18 t + 12$
3.12.22.78 $x^{12} + 24 x^{9} + 18 x^{8} - 18 x^{7} + 186 x^{6} + 324 x^{5} + 54 x^{4} + 288 x^{3} + 540 x^{2} + 270 x + 333$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 18\right) x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 18 t + 21$
3.12.22.80 $x^{12} + 30 x^{9} + 18 x^{8} - 18 x^{7} + 285 x^{6} + 378 x^{5} + 108 x^{4} + 630 x^{3} + 783 x^{2} + 108 x + 225$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 5/2]_{2}^{6}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 21\right) x^{3} + \left(9 t + 18\right) x^{2} + \left(18 t + 9\right) x + 9 t + 21$
3.12.22.92 $x^{12} + 6 x^{9} + 42 x^{6} + 54 x^{5} + 81 x^{4} + 126 x^{3} + 162 x^{2} + 225$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{3} + \left(9 t + 9\right) x^{2} + 9 t + 21$
3.12.22.94 $x^{12} + 6 x^{9} + 18 x^{8} - 18 x^{7} + 87 x^{6} + 162 x^{5} + 324 x^{4} + 288 x^{3} + 783 x^{2} - 378 x + 441$ $3$ $6$ $2$ $22$ $C_3\times S_3^2$ (as 12T70) $[5/2]$ $[2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 9\right) x^{3} + \left(9 t + 18\right) x^{2} + \left(18 t + 9\right) x + 21$
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