Let $E$ be an elliptic curve over a field $k$ given by $y^2=x^3+ax+b$. Determine how many points $P$ in $E(k)$ satisfy $2P=0$.
My thought: $2P=0 \iff P=-P\iff P\;$ lies on x-axis (since $-P$ is the reflection of $P$ over x-axis). In addition, the point at infinity also satisfies the condition. So the number of points $P$ satisfies $2P=0$ is "the number of solutions of $x^3+ax+b=0$" $+1$.
But this is a homework problem, if that is the answer, it is too straight forward. Is there any trap? Or did I do something wrong?