 Solution (source code)

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= Solution

For every prime $p\ne37$, the <elliptic-curve discriminant> is a unit modulo $p$, giving <good reduction>. <Hasse's theorem on elliptic curves> gives
$$
\boxed{\left|\#\widetilde E_p(\mathbb F_p)-(p+1)\right|\le2\sqrt p.}
$$
Equivalently, the <elliptic-curve point count over a finite field> lies between $p+1-2\sqrt p$ and $p+1+2\sqrt p$, including for $p=2$.

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