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Under the assumption $b\\neq 0$ we show that there exists $\\Q$-unirational elliptic surface contained in $\\cal{V}_{f}$. If $b=0, a<0$ and $-a\\not\\equiv 2,18,34 \\pmod {48}$ then there exists $\\Q$-rational surface contained in $\\cal{V}_{f}$. 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