From Ireland and Rosen Number theory book(ch11.#11)
Consider the curve $y^2=x^{3}-Dx$ over $\mathbb{F}_{p}$, where $D \not= 0$. Call this curve $C_{1}$. It can be shown that the substitution $x=\frac{1}{2}(u+v^{2})$ and $y=\frac{1}{2}v(u+v^{2})$ transforms $C_{1}$ into the curve $C_{2}$ given by $u^{2}-v^{4}=4D$.
My question:
How can we show that in any finite field the number of finite points on $C_{1}$ is one more than the number of points on $C_{2}$?