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On a quadratic diophantine equation

Given a quadratic diophantine equation in $\mathbb Z[x,y,z]$ of form $$ax^2+by^2+cx+dy+ez+f=0$$ are there standard methods to solve for it when $$\|(x^2,y^2,z)\|_\infty\leq e^{1/2}$$ $$\|(a,b,c,d,e,f)...