Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 24 / 3 / e / Solution

For every prime $p\ne 37$, the elliptic-curve discriminant is a unit modulo $p$, giving good reduction. Hasse's theorem on elliptic curves givesEquivalently, the elliptic-curve point count over a finite field lies between $p+1-2\sqrt{p}$ and $p+1+2\sqrt{p}$, including for $p=2$.