On the ranks of elliptic curves with isogenies

2016/11/04 by Daniels, Harris B., Goodwillie, Hannah · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.01329

Abstract

In recent years, the question of whether the ranks of elliptic curves defined over ℚ are unbounded has garnered much attention. One can create refined versions of this question by restricting one's attention to elliptic curves over ℚ with a certain algebraic structure, e.g., with a rational point of a given order. In an attempt to gather data about such questions, we look for examples of elliptic curves over ℚ with an n-isogeny and rank as large as possible. To do this, we use existing techniques due to Rogers, Rubin, Silverberg, and Nagao and develop a new technique (based on an observation made by Mazur) that is more computationally feasible when the naive heights of the elliptic curves are large.

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