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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.20.73 $x^{12} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 2$ $2$ $12$ $1$ $20$ $C_2^3:S_4$ (as 12T111) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 2$
2.12.20.80 $x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ $2$ $12$ $1$ $20$ $C_2^3:S_4$ (as 12T111) $[4/3, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$
2.12.22.129 $x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 4 x + 6$ $2$ $12$ $1$ $22$ $C_2^3:S_4$ (as 12T111) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 4 x + 6$
2.12.22.132 $x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$ $2$ $12$ $1$ $22$ $C_2^3:S_4$ (as 12T111) $[4/3, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$
2.12.25.104 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 6 x^{2} + 8 x + 10$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 6 x^{2} + 8 x + 10$
2.12.25.2 $x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$
2.12.25.46 $x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 10 x^{2} + 8 x + 6$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 10 x^{2} + 8 x + 6$
2.12.25.53 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 14 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 2 x^{4} + 14 x^{2} + 10$
2.12.25.61 $x^{12} + 4 x^{11} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 10 x^{2} + 2$
2.12.25.66 $x^{12} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 2$
2.12.25.7 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$
2.12.25.79 $x^{12} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2^3:S_4$ (as 12T111) $[4/3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 6 x^{2} + 8 x + 2$
2.12.30.310 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{2} + 10$
2.12.30.338 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 12 x^{2} + 2$
2.12.30.369 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 4 x^{2} + 8 x + 2$
2.12.30.400 $x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 14$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 14$
2.12.30.494 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 12 x^{2} + 8 x + 10$
2.12.30.515 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{2} + 8 x + 2$
2.12.30.532 $x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 8 x + 2$
2.12.30.559 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 12 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_2^3:S_4$ (as 12T111) $[8/3, 10/3]$ $[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 12 x^{2} + 8 x + 2$
2.12.33.407 $x^{12} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$
2.12.33.419 $x^{12} + 10 x^{10} + 8 x^{9} + 4 x^{6} + 12 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 10 x^{10} + 8 x^{9} + 4 x^{6} + 12 x^{4} + 4 x^{2} + 2$
2.12.33.448 $x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$
2.12.33.459 $x^{12} + 10 x^{10} + 4 x^{6} + 12 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 10 x^{10} + 4 x^{6} + 12 x^{4} + 4 x^{2} + 2$
2.12.33.464 $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{4} + 4 x^{2} + 2$
2.12.33.469 $x^{12} + 2 x^{10} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$
2.12.33.492 $x^{12} + 14 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 14 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 4 x^{2} + 8 x + 2$
2.12.33.521 $x^{12} + 10 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 10 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 2$
2.12.33.532 $x^{12} + 6 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$
2.12.33.552 $x^{12} + 6 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$
2.12.33.622 $x^{12} + 2 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 10$
2.12.33.644 $x^{12} + 10 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 10 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 x^{2} + 8 x + 10$
2.12.33.667 $x^{12} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$
2.12.33.677 $x^{12} + 14 x^{10} + 8 x^{9} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 14 x^{10} + 8 x^{9} + 12 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.12.33.746 $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{7} + 12 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{7} + 12 x^{4} + 4 x^{2} + 2$
2.12.33.753 $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $33$ $C_2^3:S_4$ (as 12T111) $[8/3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 2$
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