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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.18.83 $x^{12} - 6 x^{11} + 51 x^{10} - 30 x^{9} + 117 x^{8} - 36 x^{7} + 60 x^{6} + 252 x^{5} - 36 x^{4} + 288 x^{3} + 360$ $3$ $6$ $2$ $18$ $C_3:S_3^2$ (as 12T71) $[2]$ $[3/2, 3/2, 2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + 3 x^{4} + 6 t x^{3} + 18 t + 12$
3.12.22.17 $x^{12} - 12 x^{9} + 18 x^{7} + 366 x^{6} + 324 x^{5} + 297 x^{4} + 774 x^{3} + 486 x^{2} + 378 x + 333$ $3$ $6$ $2$ $22$ $C_3:S_3^2$ (as 12T71) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(18 t + 12\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 18\right) x + 18 t + 21$
3.12.22.20 $x^{12} + 36 x^{9} - 18 x^{8} + 366 x^{6} - 108 x^{5} + 621 x^{4} + 864 x^{3} + 594 x^{2} + 324 x + 90$ $3$ $6$ $2$ $22$ $C_3:S_3^2$ (as 12T71) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 24\right) x^{3} + \left(18 t + 9\right) x^{2} + \left(18 t + 18\right) x + 9 t + 12$
3.12.22.75 $x^{12} - 48 x^{9} + 18 x^{7} + 1122 x^{6} + 864 x^{5} - 108 x^{4} + 1584 x^{3} + 729 x^{2} - 270 x + 549$ $3$ $6$ $2$ $22$ $C_3:S_3^2$ (as 12T71) $[5/2]$ $[3/2, 2, 5/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 24 t x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 18 t + 3$
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