We develop an algorithm to determine a one-parameter family of elliptic curves associated to a one-parameter family of K3 surfaces with generic Picard number 19 by a Shioda-Inose structure. The family of elliptic curves is determined up to an isomorphism and an isogeny. An application to a generalized congruence number problem is also discussed. © 2004 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Number Theory
Long, L. (2004). On Shioda-Inose structures of one-parameter families of K3 surfaces. Journal of Number Theory, 109 (2), 299-318. https://doi.org/10.1016/j.jnt.2004.06.009