What is the smallest prime $p$ for which there exists a quadratic form
$$Q=aX^2+bY^2+cZ^2 \quad (a,b,c \in \mathbf F_p \setminus \{0\} )$$
such that the conic $\{Q=0\}$ has no points in $\mathbf P^2(\mathbf F_p)$?
(This may well be judged "not research-level". For what it's worth, I searched online and asked a couple of colleagues, but without success.)