Suppose $\mathcal{E}$ is an elliptic curve defined over $\mathbb{Q}$,
Then Hasse's theorem states that for any large characteristic $p$ there exists an algebraic number $\lambda_p$ of modulus $\sqrt{p}$ with
$$ \sharp({\mathcal{E}/\mathbb{F}_p}) = p -\lambda_p -\overline{\lambda_p} +1. $$
Can we construct an elliptic curve $\mathcal{E}'$ such that for large enough primes $p$ we have $$ \sharp({\mathcal{E}'/\mathbb{F}_p}) = p +\lambda_p +\overline{\lambda_p} +1 \ \ ? $$
If not in general, are there any conditions which allow such a construction ? (e.g. $\mathcal{E}$ has CM.)