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Results (5 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.8.12 $x^{8} - 2 x^{6} - 2 x^{5} + 8 x^{4} + 8 x^{3} - 4 x + 4$ $2$ $4$ $2$ $8$ $A_4\wr C_2$ (as 8T42) $[4/3, 4/3]$ $[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ $t^{2} + t + 1$ $x^{4} + 2 t x^{2} + 2 t x + 2$
2.8.16.25 $x^{8} - 4 x^{5} + 8 x^{4} + 16 x^{2} + 8 x + 28$ $2$ $4$ $2$ $16$ $A_4\wr C_2$ (as 8T42) $[8/3, 8/3]$ $[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ $t^{2} + t + 1$ $x^{4} + 4 t x + 4 t + 6$
2.8.16.26 $x^{8} + 8 x^{7} + 24 x^{6} + 36 x^{5} + 44 x^{4} + 64 x^{3} + 64 x^{2} + 24 x + 36$ $2$ $4$ $2$ $16$ $A_4\wr C_2$ (as 8T42) $[8/3, 8/3]$ $[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 4 x^{2} + \left(4 t + 4\right) x + 6$
2.8.16.27 $x^{8} + 8 x^{7} + 12 x^{6} - 20 x^{5} + 12 x^{4} + 80 x^{3} - 8 x^{2} - 24 x + 36$ $2$ $4$ $2$ $16$ $A_4\wr C_2$ (as 8T42) $[8/3, 8/3]$ $[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 4 t x^{2} + 4 t x + 6$
2.8.16.28 $x^{8} - 4 x^{5} + 16 x^{2} + 24 x + 12$ $2$ $4$ $2$ $16$ $A_4\wr C_2$ (as 8T42) $[8/3, 8/3]$ $[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ $t^{2} + t + 1$ $x^{4} + 4 t x + 4 t + 2$
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