L-values for conductor 32

In recent years, Rogers and Zudilin developed a method to write L-values attached to elliptic curves as periods. In order to apply this method to a broader collection of L-values, we study Eisenstein series and determine their Fourier series at cusps. Subsequently, we write the L-values of an elliptic curve of conductor 32 as an integral of Eisenstein series and evaluate the value at k > 1 explicitly as a period. As a side result, we give simple integral expressions for the generating functions of L(E, k) when even (or odd) k runs over positive integers. (c) 2021 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).