Let $E$ be a semistable elliptic curve over $\mathbb{Q}$, and let $N$ be the conductor of $E$. Then there exists a normalized cuspidal newform $f \in S_2(\Gamma_0(N))$ of weight $2$ and level $\Gamma_0(N)$ such that
paragraph
admin
\begin{align*}
L(E,s) = L(f,s).
\end{align*}
latex_env
admin
Equivalently, the Hasse-Weil $L$-function of $E$ agrees with the Hecke $L$-function of $f$.