A note on log-algebraicity on elliptic curves

TL;DR

This paper explores log-algebraic identities related to elliptic curves over rationals, derived from modular parametrizations, and examines their implications for special values of elliptic curve L-functions.

Contribution

It provides new insights into log-algebraic power series identities for elliptic curves and their applications to elliptic L-functions.

Findings

Identified new log-algebraic identities for elliptic curves.

Connected these identities to special values of elliptic L-functions.

Enhanced understanding of modular parametrizations in elliptic curve theory.

Abstract

We analyze log-algebraic power series identities for formal groups of elliptic curves over $\mathbb{Q}$ which arise from modular parametrizations. We further investigate applications to special values of elliptic curve $L$-functions.