On Zagier's Conjecture for Base Changes of Elliptic Curves

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 $F$.

2010 Mathematics Subject Classification: 11G40, 11G55, 19F27

Keywords and Phrases: Elliptic curves, $L$-functions, elliptic dilogarithm, Zagier's conjecture, regulators, Beilinson's conjecture

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