Modular Forms and Elliptic Curves over the Field of Fifth Roots of Unity

Abstract

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.

2000 AMS Subject Classification:

• Primary 11F75
• Secondary 11F67
• 11G05
• 11Y99

Keywords:

• automorphic forms
• cohomology of arithmetic groups
• Hecke operators
• elliptic curves

Notes

¹More precisely, in [Ash et al. 02, §3], the authors work with the equivariant cohomology , but this is isomorphic to , since has characteristic zero.