In this thesis, we shall prove the Eichler-Shimura theory.
For this, we shall introduce the moduar forms and cusp forms for SL(2,Z) and Γ_0(N)$ respectively. And we will associate an L-function and introduce Hecke operators as a tool for expanding the L-functions and an L-function for the elliptic curve. And then we shall prove the main theorem by using the isogeny and the Jacobian variety.
