  Lattices are simplified by removing some of their doubly irreducible
elements, resulting in smaller lattices called racks. All vertically
indecomposable modular racks of $n \le 40$ elements are listed, and the numbers
of all modular lattices of $n \le 40$ elements are obtained by P\'olya
counting. SageMath code is provided that allows easy access both to the listed
racks, and to the modular lattices that were not listed. More than 3000-fold
savings in storage space are demonstrated.
