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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.14.1 $x^{12} - 6 x^{8} - 6 x^{6} + 18 x^{4} + 36 x^{2} + 18$ $3$ $6$ $2$ $14$ $(C_3\times C_3):C_4$ (as 12T17) $[3/2]$ $[3/2, 3/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + 3 t x^{2} + 3 t$
3.12.14.14 $x^{12} - 6 x^{8} - 6 x^{6} + 45 x^{4} + 54 x^{2} + 18$ $3$ $6$ $2$ $14$ $(C_3\times C_3):C_4$ (as 12T17) $[3/2]$ $[3/2, 3/2]_{2}^{2}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{2} + 3 t$
3.12.16.22 $x^{12} + 12 x^{11} + 72 x^{10} + 192 x^{9} + 324 x^{8} + 432 x^{7} + 2808 x^{6} - 3240 x^{5} + 12312 x^{4} - 12528 x^{3} + 121824 x^{2} + 517428$ $3$ $3$ $4$ $16$ $(C_3\times C_3):C_4$ (as 12T17) $[2]$ $[2, 2]^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x^{2} + 9 t^{3} + 9 t^{2} + 18 t + 12$
3.12.16.37 $x^{12} - 6 x^{11} + 60 x^{10} - 10 x^{9} + 603 x^{8} + 3924 x^{7} + 16740 x^{6} + 36078 x^{5} + 108120 x^{4} + 201600 x^{3} + 381102 x^{2} + 225588 x + 200729$ $3$ $3$ $4$ $16$ $(C_3\times C_3):C_4$ (as 12T17) $[2]$ $[2, 2]^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$
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