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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.16.27 $x^{12} + 24 x^{11} + 198 x^{10} + 624 x^{9} + 837 x^{8} + 1512 x^{7} + 12690 x^{6} + 13608 x^{5} + 49410 x^{4} - 22248 x^{3} - 219024 x^{2} + 185733$ $3$ $3$ $4$ $16$ $C_3^3:C_4$ (as 12T72) $[2]$ $[2, 2, 2]^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t^{3} + 18 t^{2} + 18 t + 3$
3.12.16.46 $x^{12} - 24 x^{11} + 216 x^{10} + 804 x^{9} + 1944 x^{8} + 11664 x^{7} + 33912 x^{6} + 37584 x^{5} + 295488 x^{4} + 32184 x^{3} + 981072 x^{2} + 1122984$ $3$ $3$ $4$ $16$ $C_3^3:C_4$ (as 12T72) $[2]$ $[2, 2, 2]^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6\right) x^{2} + 9 t^{3} + 18 t + 12$
3.12.18.43 $x^{12} - 6 x^{11} + 12 x^{10} + 48 x^{9} + 81 x^{8} + 54 x^{7} + 48 x^{6} - 72 x^{5} - 54 x^{4} - 72 x^{3} + 234$ $3$ $6$ $2$ $18$ $C_3^3:C_4$ (as 12T72) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 3 t x^{5} + \left(6 t + 3\right) x^{4} + 3 t x^{3} + 3 t + 18$
3.12.18.70 $x^{12} - 6 x^{10} + 6 x^{9} + 45 x^{8} + 18 x^{7} + 12 x^{6} + 270 x^{4} + 108 x^{3} + 450$ $3$ $6$ $2$ $18$ $C_3^3:C_4$ (as 12T72) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{4} + \left(3 t + 6\right) x^{3} + 21 t + 18$
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