Introduction to Elliptic Curves and Modular Forms Introduction to Elliptic Curves and
Modular Forms …

… introductory article provides an account of the recent history of the field of elliptic genera
and elliptic … , an especially relevant topic for the study of elliptic genera, to be included in this …

… elliptic curves and certain modular forms, and justify which modular forms correspond to elliptic
curves… In this chapter, we introduce elliptic curves, modular forms and Lfunctions through …

… vi Geometric Modular Forms and Elliptic Curves … and Galois representations of elliptic
modular forms in this book). We should also note that automorphic Galois representations for …

… introduce elliptic curves as certain smooth curves in P2. We then consider the group law on
their points and formulate an equivalent definition of elliptic curves … a pointed curve of genus …

… by modular forms of weight 1. … from modular forms. This is the famous Shimura-Taniyama-Weil
conjecture, which can be phrased also in terms of modular uniformization of elliptic curves…

… In Chapter 10 we introduce modular forms for subgroups of … modular forms appear in the
so-called arithmetic modularity … our geometric interpretation of modular forms. In this chapter we …

… complicated than elliptic curves; further applications of our formulas for modular curves and
… ); since ω has no zeros in the upper half-plane, any modular form ε of weight 2 with w∗ε = −ε …

… Elliptic curves are intimately connected with the theory of modular forms, in more ways than
one. In the early sections I have tried to give a brief introduction to the fundamentals of the …

… cusp forms of weight two for Hecke subgroups of the modular group to rational elliptic curves…
Under this construction, the L function of the cusp form (which is an automorphic L function) …