Finding Elliptic Curves With Many Integral Points
Number Theory
2020-12-14 v1
Abstract
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.
Cite
@article{arxiv.2012.06233,
title = {Finding Elliptic Curves With Many Integral Points},
author = {Benjamin Jones},
journal= {arXiv preprint arXiv:2012.06233},
year = {2020}
}
Comments
23 pages, 2 figures, 5 tables. See ancillary Magma files containing complete search results