2109202313:47 tags: # Hasse's Theorem The Hasse Theorem is used to get an approximation of how many points are on an EC defined over $F_P$. (see also [[Elliptic Curve over Finite Fields]]) Let $E$ an EC over $\mathbb{F_p}$. Then $\#E(\mathbb{F_p})=p+1-t_p\text{ with }t_p\text{ satisfy }|t_p| \leq 2\sqrt p$. $t_p$ is called the **trace of Frobenius** for $E/\mathbb{F_p}$. It means that the numbers of points over will be between $p+1-2\sqrt p$ and $p+1+2\sqrt p$. --- ## References 1. [[2. Literature notes/Elliptic Curves in Finite Fields]]