##  [Modularity Theorem](/modularity-theorem) 

  ##  [Modularity Theorem](https://puremath.quantumdictionary.io/modularity-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem asserting that every elliptic curve defined over Q is modular: its Hasse–Weil L-function equals the L-function of a weight-two cuspidal newform of level equal to the curve's conductor, establishing a correspondence between rational elliptic curves and certain modular forms.