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High Rank Elliptic Curves with Torsion Z/4Z induced by Kihara’s Curves

Published

Author(s)

Foad Khoshnam, Dustin Moody

Abstract

Working over the field Q(t), Kihara constructed an elliptic curve with torsion group Z/4Z and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves with torsion group Z/4Z and rank at least five. This matches the current record for such curves. In addition, we give specific examples of these curves with ranks 10 and 11.
Citation
INTEGERS, The electronic journal of combinatorial number theory
Volume
16

Keywords

elliptic curves, torsion, rank
Created October 5, 2016, Updated April 12, 2017