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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.20.61 $x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$ $2$ $12$ $1$ $20$ $C_4^2:D_6$ (as 12T115) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$
2.12.20.77 $x^{12} + 2 x^{11} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$ $2$ $12$ $1$ $20$ $C_4^2:D_6$ (as 12T115) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$
2.12.22.84 $x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 2$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T115) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 2$
2.12.22.88 $x^{12} + 2 x^{11} + 4 x^{8} + 6 x^{6} + 2 x^{4} + 6 x^{2} + 2$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T115) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 4 x^{8} + 6 x^{6} + 2 x^{4} + 6 x^{2} + 2$
2.12.25.102 $x^{12} + 4 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 10$
2.12.25.107 $x^{12} + 2 x^{4} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{4} + 10 x^{2} + 2$
2.12.25.127 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$
2.12.25.38 $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 14 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 14 x^{2} + 2$
2.12.25.4 $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 2 x^{4} + 10 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 2 x^{4} + 10 x^{2} + 10$
2.12.25.48 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 14$
2.12.25.91 $x^{12} + 2 x^{4} + 2 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{4} + 2 x^{2} + 8 x + 2$
2.12.25.97 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T115) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 10 x^{2} + 10$
2.12.32.142 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{4} + 4 x^{2} + 10$
2.12.32.15 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.241 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 14$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 14$
2.12.32.278 $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$
2.12.32.313 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 10$
2.12.32.343 $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 12 x^{6} + 12 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 12 x^{6} + 12 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.35 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.498 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T115) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$
2.12.33.421 $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 4 x^{6} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 4 x^{6} + 12 x^{2} + 2$
2.12.33.491 $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$
2.12.33.542 $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$
2.12.33.545 $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 2$
2.12.33.571 $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$
2.12.33.590 $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{6} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{6} + 4 x^{2} + 2$
2.12.33.670 $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$
2.12.33.702 $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$
2.12.33.711 $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 4 x^{8} + 8 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$
2.12.33.721 $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 10$
2.12.33.737 $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{5} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{5} + 8 x^{3} + 4 x^{2} + 2$
2.12.33.741 $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{6} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{6} + 12 x^{2} + 2$
2.12.33.751 $x^{12} + 4 x^{11} + 14 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 14 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$
2.12.33.826 $x^{12} + 4 x^{11} + 14 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 14 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$
2.12.33.862 $x^{12} + 4 x^{11} + 14 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 14 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$
2.12.33.882 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T115) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$
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