One of the promising directions in number theory is the construction of polynomial primality tests for integers. Such tests can be used in cryptography to improve modern encryption protocols. In the article \textquotedblleft On the Baillie PSW Conjecture\textquotedblright\ we considered a combined primality test based on verifying two conditions: Fermat's little theorem $2^{n-1}\equiv 1(\bmod\ n)$ and Lucas' theorem $F_{n+1}\equiv 0(\bmod\ n)$, where $F_n$ is the $n$-th term of the Fibonacci sequence for numbers $n\equiv\pm 2(\bmod\ 5)$. Odd composite numbers passing this combined test were called FL-pseudoprimes. We established strong restrictions on FL-pseudoprimes and proved that none of them exist in the interval up to $10^{23}$. In the article \textquotedblleft In the present paper, we consider a combination of the Fermat test with a primality test based on elliptic curves over finite fields. This test works successfully for odd integers of a special form, namely, $n\equiv 2(\bmod\ 3)$, for which we formulate a hypothesis analogous to the Baillie-PSW hypothesis.