According to the theorem of Mazur (1977), The torsion subgroup of the group of rational points $E(Q)$ on an elliptic curve must be one of the following 15 groups:
$C_N$ with $1 ≤ N ≤ 10$ or $N = 12,$
$C_2 × C_{2N}$ with $1 ≤ N ≤ 4$. In particular, $E(Q)_{tors}$ has order at most 16. I want to check whether my understanding is correct. Let $O$ be the point in infinity.
Does this mean for any point $P \in E(Q)$ of finite order, $m \leq 16$ where $mP=O$? In other words scalar multiple of points of finite order can't be bigger than 16?