Modular form associated to an elliptic curve/Q\mathbb Q (reviewed)

For every elliptic curve over $\Q$ of conductor $N$, there is a unique weight $2$ newform for $\Gamma_0(N)$ with the same L-function. This was proved by Breuil, Conrad, Diamond, and Taylor, building on the proof of Fermat's last theorem by Wiles and Taylor-Wiles.