Computations in non-commutative Iwasawa theory

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension Q(mu(p)infinity, (p infinity)root m)/Q. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative lwasawa theory.