Abstract
In this note, we announce some results concerning the existence of a rational elliptic surface having a given structure of the Mordell-Weil lattice, which has been classified in [5]. With some arithmetic applications in mind, we consider the question over the rational number field Q. Details will be given in forthcoming papers. For general facts on Mordell-Weil lattices (MWL), we refer to [7] or [8].
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