## On Zagier's conjecture for base changes of elliptic curves

### Summary

Summary: Let $E$ be an elliptic curve over Q, and let $F$ be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for $L(E_F,2)$, where $E_F$ is the base change of $E$ to $F$.

### Mathematics Subject Classification

11G40, 11G55, 19F27

### Keywords/Phrases

elliptic curves, $L$-functions, elliptic dilogarithm, Zagier's conjecture, regulators, Beilinson's conjecture