Let $q = p^{n}$ and let $E$ be an elliptic curve. Hasse's bound tell us that $$ |\sharp E(\mathbb{F}_{q}) - q - 1| \leq 2\sqrt{q} $$ for any $q$. We can prove this without using Weil conjecture for elliptic curves.
But I heard that Hasse's bound is equivalent to Weil conjecture for elliptic curves. I know weil conjecutre deduces this inequality, but how this conjecture deduce Weil conjecture for elliptic curves?
Any reference is also appreciated, thank you.