  The cluster lens Cl 0024+1654 is undoubtedly one of the most beautiful
examples of strong gravitational lensing, providing five large images of a
single source with well-resolved substructure. Using the information contained
in the positions and the shapes of the images, combined with the null space
information, a non-parametric technique is used to infer the strong lensing
mass map of the central region of this cluster. This yields a strong lensing
mass of 1.60x10^14 M_O within a 0.5' radius around the cluster center. This
mass distribution is then used as a case study of the monopole degeneracy,
which may be one of the most important degeneracies in gravitational lensing
studies and which is extremely hard to break. We illustrate the monopole
degeneracy by adding circularly symmetric density distributions with zero total
mass to the original mass map of Cl 0024+1654. These redistribute mass in
certain areas of the mass map without affecting the observed images in any way.
We show that the monopole degeneracy and the mass-sheet degeneracy together lie
at the heart of the discrepancies between different gravitational lens
reconstructions that can be found in the literature for a given object, and
that many images/sources, with an overall high image density in the lens plane,
are required to construct an accurate, high-resolution mass map based on
strong-lensing data.
