Lower bound for the $2$-adic valuations of central $L$-values of elliptic curves with complex multiplication

Keiichiro Nomoto

Published 2022-07-21Version 1

Let $E_{4D}$ be the elliptic curve $y^2=x^3-4Dx$ defined over $K=\mathbb{Q}(i)$ for $D\in K$ which is coprime to $2$. In this paper, we give a sharp lower bound for the $2$-adic valuation of the algebraic part of the central value of Hecke $L$-function associated with $E_{4D}$.