  In this paper we construct parameterizations of elliptic curves over the
rationals which have many consecutive integral multiples. Using these
parameterizations, we perform searches in GMP and Magma to find curves with
points of small height, curves with many integral multiples of a point, curves
with high multiples of a point integral, and over two hundred curves with more
than one hundred integral points. In addition, a novel and complete
classification of "self-descriptive numbers" is constructed by bounding the
number of zeros such a number must contain.
