Birational transformations of certain quartic surfaces

1. Statement of the problem. It has been shown by Enriquest that if an algebraic surface contains a pencil of elliptic curves and also two curves cutting each curve of the pencil in two groups of points which are not equivalent and which do not possess equivalent multiples, the surface is invariant under a discontinuous infinite series of birational transformations. In a more recent memoir: the same author states that, with the exception of the case in which