Let $F_p$ be a finite field and $p\equiv 3 \pmod 4$, and $a,c$ are non-square elements in $F_p$. I want to parametrize the conic:

$$cy^2=-3x^2-2ax-16a$$

($-1$ and $3$ are non-squares in this field as well). Would you please help me to do that. Actualy I can not find a point on this conic to use it to parametrize it. I want to define an encoding function from F_p to a Douche-Icart-Kohel curve and I need to map every t in F_p to the curve, and in the middle at first I should find a point on the conic. Thank you in advanced.