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Results (14 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.18.60 $x^{12} + 10 x^{10} + 6 x^{8} + 8 x^{7} + 8 x^{6} - 48 x^{5} + 44 x^{4} - 64 x^{3} - 8 x^{2} - 24$ $2$ $4$ $3$ $18$ $C_2^2 \times A_4$ (as 12T26) $[2, 2]$ $[2, 2, 2]^{6}$ $t^{3} + t + 1$ $x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 2$
2.12.18.62 $x^{12} + 10 x^{10} + 18 x^{8} + 8 x^{7} + 72 x^{6} - 16 x^{5} + 204 x^{4} + 248 x^{2} + 248$ $2$ $4$ $3$ $18$ $C_2^2 \times A_4$ (as 12T26) $[2, 2]$ $[2, 2, 2]^{6}$ $t^{3} + t + 1$ $x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 6$
2.12.24.110 $x^{12} - 8 x^{11} + 28 x^{10} + 64 x^{9} + 166 x^{8} + 296 x^{7} + 912 x^{6} + 704 x^{5} + 2212 x^{4} + 784 x^{3} + 3424 x^{2} + 928 x + 3576$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + 4 t^{2} x^{3} + \left(6 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 12 t + 14$
2.12.24.143 $x^{12} + 12 x^{11} + 56 x^{10} + 128 x^{9} + 202 x^{8} + 408 x^{7} + 896 x^{6} + 1584 x^{5} + 1988 x^{4} + 1888 x^{3} + 2064 x^{2} - 64 x + 2376$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + 4 x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + 4 t x + 8 t^{2} + 12 t + 10$
2.12.24.158 $x^{12} + 4 x^{11} - 4 x^{10} + 64 x^{9} + 150 x^{8} + 456 x^{7} + 1216 x^{6} + 1296 x^{5} + 1460 x^{4} + 2976 x^{3} + 352 x^{2} + 960 x + 632$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t^{2} x + 8 t^{2} + 12 t + 6$
2.12.24.160 $x^{12} + 20 x^{10} - 8 x^{9} + 98 x^{8} + 56 x^{7} + 448 x^{6} + 736 x^{5} + 1588 x^{4} + 1424 x^{3} + 1408 x^{2} + 128 x + 424$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + 4 t x^{3} + \left(4 t^{2} + 2 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 10$
2.12.24.219 $x^{12} - 8 x^{11} + 88 x^{10} - 88 x^{9} + 450 x^{8} - 120 x^{7} + 504 x^{6} + 336 x^{5} + 116 x^{4} + 368 x^{3} + 128 x^{2} + 32 x + 72$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(2 t^{2} + 4\right) x^{2} + 4 t x + 4 t^{2} + 2$
2.12.24.249 $x^{12} + 4 x^{11} + 60 x^{10} + 280 x^{9} + 322 x^{8} + 88 x^{7} - 168 x^{6} - 160 x^{5} + 68 x^{4} + 64 x^{3} + 16 x^{2} + 8$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(2 t^{2} + 4 t\right) x^{2} + 4 t x + 2$
2.12.24.264 $x^{12} - 6 x^{10} + 12 x^{9} + 10 x^{8} + 24 x^{7} + 472 x^{6} + 224 x^{5} + 1036 x^{4} + 1232 x^{3} + 1752 x^{2} + 336 x - 104$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 3]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(6 t^{2} + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 12 t + 6$
2.12.24.276 $x^{12} + 30 x^{10} - 20 x^{9} + 134 x^{8} + 440 x^{7} + 840 x^{6} + 1472 x^{5} + 1500 x^{4} + 1776 x^{3} + 1736 x^{2} + 1744 x + 1768$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 3]^{6}$ $t^{3} + t + 1$ $x^{4} + 4 t x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 10$
2.12.24.308 $x^{12} + 14 x^{10} + 4 x^{9} + 142 x^{8} + 104 x^{7} + 696 x^{6} + 816 x^{5} + 2508 x^{4} + 2608 x^{3} + 4872 x^{2} + 3344 x + 3624$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 3]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(2 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 8 t + 10$
2.12.24.320 $x^{12} - 8 x^{11} + 16 x^{10} + 48 x^{9} + 430 x^{8} + 424 x^{7} + 496 x^{6} + 16 x^{5} + 1732 x^{4} + 1776 x^{3} + 3248 x^{2} - 384 x + 3032$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 4\right) x^{2} + 4 t x + 12 t + 14$
2.12.24.46 $x^{12} + 28 x^{10} - 24 x^{9} - 34 x^{8} - 248 x^{7} + 248 x^{6} + 288 x^{5} + 1988 x^{4} + 2064 x^{3} + 4272 x^{2} + 1856 x + 2264$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 2, 3]^{3}$ $t^{3} + t + 1$ $x^{4} + 4 t x^{3} + \left(6 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 4 t + 14$
2.12.24.67 $x^{12} + 4 x^{11} + 82 x^{10} + 364 x^{9} + 774 x^{8} + 1416 x^{7} + 2472 x^{6} + 3120 x^{5} + 4012 x^{4} + 2816 x^{3} + 2456 x^{2} + 752 x + 424$ $2$ $4$ $3$ $24$ $C_2^2 \times A_4$ (as 12T26) $[2, 3]$ $[2, 2, 3]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 10$
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