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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.20.59 $x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 6 x^{4} + 6 x^{2} + 6$ $2$ $12$ $1$ $20$ $C_4^2:D_6$ (as 12T114) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 6 x^{4} + 6 x^{2} + 6$
2.12.20.60 $x^{12} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$ $2$ $12$ $1$ $20$ $C_4^2:D_6$ (as 12T114) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$
2.12.22.89 $x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T114) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6$
2.12.22.97 $x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 6$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T114) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 6$
2.12.25.101 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 14 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 14 x^{2} + 14$
2.12.25.112 $x^{12} + 4 x^{10} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 8 x + 14$
2.12.25.39 $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 2$
2.12.25.55 $x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 14 x^{2} + 8 x + 2$
2.12.25.60 $x^{12} + 4 x^{10} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 2$
2.12.25.73 $x^{12} + 2 x^{4} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{4} + 2 x^{2} + 2$
2.12.25.76 $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 2 x^{4} + 2 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 2 x^{4} + 2 x^{2} + 10$
2.12.25.78 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 14 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_4^2:D_6$ (as 12T114) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 14 x^{2} + 8 x + 2$
2.12.32.122 $x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.16 $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.214 $x^{12} + 6 x^{10} + 4 x^{9} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$
2.12.32.216 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 4 x^{4} + 4 x^{2} + 8 x + 6$
2.12.32.252 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 10$
2.12.32.258 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 12 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 12 x^{2} + 10$
2.12.32.486 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.12.32.489 $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 4 x^{4} + 12 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T114) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 4 x^{4} + 12 x^{2} + 10$
2.12.33.418 $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$
2.12.33.437 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 10$
2.12.33.506 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$
2.12.33.528 $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 2$
2.12.33.550 $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$
2.12.33.551 $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{6} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{6} + 4 x^{2} + 2$
2.12.33.564 $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 10$
2.12.33.595 $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$
2.12.33.634 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 12 x^{2} + 2$
2.12.33.657 $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 10$
2.12.33.729 $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$
2.12.33.730 $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$
2.12.33.748 $x^{12} + 4 x^{11} + 6 x^{10} + 12 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 12 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$
2.12.33.812 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 2$
2.12.33.822 $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{6} + 12 x^{2} + 2$
2.12.33.848 $x^{12} + 4 x^{11} + 6 x^{10} + 12 x^{8} + 12 x^{6} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_4^2:D_6$ (as 12T114) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 12 x^{8} + 12 x^{6} + 4 x^{2} + 8 x + 10$
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