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Results (8 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.18.12 $x^{12} + 6 x^{11} + 3 x^{10} - 18 x^{9} + 18 x^{8} + 18 x^{7} - 3 x^{6} - 36 x^{5} + 90 x^{4} + 54 x^{3} + 117$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{5} + 3 t x^{4} + \left(3 t + 3\right) x^{3} + 9 t + 3$
3.12.18.16 $x^{12} + 6 x^{11} + 12 x^{10} + 18 x^{8} + 42 x^{6} + 126 x^{5} - 126 x^{4} + 441$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{5} + 3 t x^{4} + 21$
3.12.18.18 $x^{12} + 6 x^{11} + 24 x^{10} + 36 x^{9} + 18 x^{8} + 6 x^{6} + 72 x^{5} + 72 x^{4} + 90$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{5} + \left(3 t + 6\right) x^{4} + 9 t + 12$
3.12.18.24 $x^{12} + 6 x^{10} - 6 x^{9} + 18 x^{8} + 18 x^{7} + 69 x^{6} + 126 x^{4} + 36 x^{3} + 225$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 3\right) x^{3} + 9 t + 21$
3.12.18.25 $x^{12} + 12 x^{11} + 30 x^{10} - 36 x^{9} + 45 x^{8} - 12 x^{6} - 72 x^{5} + 144 x^{4} + 117$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$
3.12.18.3 $x^{12} - 6 x^{11} + 39 x^{10} + 90 x^{9} + 45 x^{8} - 12 x^{6} + 144 x^{5} + 144 x^{4} + 117$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$
3.12.18.34 $x^{12} + 6 x^{10} + 18 x^{8} + 36 x^{7} + 6 x^{6} + 18 x^{4} + 216 x^{3} + 549$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 6\right) x^{3} + 18 t + 3$
3.12.18.50 $x^{12} + 12 x^{11} + 24 x^{10} - 60 x^{9} + 144 x^{8} - 72 x^{7} + 6 x^{6} - 180 x^{5} + 396 x^{4} - 180 x^{3} + 549$ $3$ $6$ $2$ $18$ $C_3^4:(C_2\times C_4)$ (as 12T171) $[2]$ $[3/2, 3/2, 2, 2]_{2}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + 6 t x^{4} + 6 x^{3} + 18 t + 3$
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