elementary number theory – Hilbert’s Tenth Problem

I know that Hilbert’s Tenth problem is uncomputable as shown by Matiyasevich’s theorem, but for a special case, is Hilbert’s tenth problem decidable for degree two homogenous $3$ variable instance of the problem? In other words is $ax^2+by^2+cz^2=0$ has a non trivial zero $in mathbb{Z^3}$ decidable?