b
= b
{scope}
The curve has <good reduction> at $2$ and $3$ because its discriminant $-53$ is a unit at both primes. Direct counting gives
$$
\#\widetilde E(\mathbb F_2)=4,
\qquad
\#\widetilde E(\mathbb F_3)=7.
$$
Indeed, at $p=2$ the affine solution counts for $x=0,1$ are $2,1$, and at $p=3$ the counts for $x=0,1,2$ are $2,2,2$; in each case one then adds the point at infinity.