Kummer sandwich theorem of certain elliptic K3 surfaces

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Lattice polarized K3 surfaces and Siegel modular forms (2010, methodology): “In the case of K3 surfaces polarized by the lattice H⊕ E8 ⊕ E8, explicit formulas were given previously by the authors [5] as well as Shioda [38].”
Elliptic Surfaces (2009, background): “Shioda showed in [98] that X ′ returns in fact the Kummer surface Km(E × E ) from the Shioda-Inose structure – we have identified the singular fibres in the double Kummer pencil in Example 12.”
K3 Surfaces Associated with Curves of Genus Two (2007, methodology): “Here we check that the formulas we obtain degenerate to those of Shioda [29] for the elliptic K3 surface corresponding to the Kummer surface of a product of two elliptic curves, over an algebraically closed base field.”
K3 surfaces and equations for Hilbert modular surfaces (2012, background): “has a Shioda–Inose structure, making it 2-isogenous with a product of two elliptic curves [Inose 1978; Shioda 2006; Kuwata and Shioda 2008; Clingher and Doran 2007; Elkies ≥ 2015].”