论文标题
找到具有许多积分点的椭圆曲线
Finding Elliptic Curves With Many Integral Points
论文作者
论文摘要
在本文中，我们在有许多连续的积分倍数上构造了椭圆曲线的参数化。使用这些参数化，我们在GMP和MAGMA中执行搜索，以找到具有较小高度的曲线，曲线具有许多积分的积分倍数，具有点积分的高倍数的曲线以及一百多个积分点以上的曲线。此外，通过界定必须包含的零的数量来构建“自我描述数字”的新颖而完整的分类。
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.
