Khoshnam, F.
and Moody, D.
(2016),
High Rank Elliptic Curves with Torsion Z/4Z induced by Kihara’s Curves, INTEGERS, The electronic journal of combinatorial number theory, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=922952
(Accessed November 3, 2025)
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High Rank Elliptic Curves with Torsion Z/4Z induced by Kihara's Curves
Published
Author(s)
Foad Khoshnam,
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
Pub Type
Journals
Download Paper
Keywords
elliptic curves, torsion, rank
Citation
Issues
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Created October 4, 2016, Updated October 12, 2021