High-rank elliptic curves with given torsion group and some applications
Volume 126 / 2023
Banach Center Publications 126 (2023), 9-26
MSC: Primary 11G05; Secondary 11Y05
DOI: 10.4064/bc126-1
Abstract
In this survey paper, we describe several methods for constructing elliptic curves with a given torsion group and high rank over the rationals and quadratic fields. We also discuss potential applications of such curves in the elliptic curve factorization method and their role in the construction of rational Diophantine sextuples.
