A two-parametric family of high rank Mordell curves
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Published:2023-11-18
Issue:
Volume:
Page:1-9
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ISSN:1793-0421
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Container-title:International Journal of Number Theory
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language:en
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Short-container-title:Int. J. Number Theory
Affiliation:
1. Ahva St. 15/14, Haifa, Israel
Abstract
We present an elementary construction of an explicit two-parametric family of elliptic curves over [Formula: see text] of the form [Formula: see text] such that the rank of each member of the family is at least seven. The main new ingredient is Ramanujan’s identity for sums of rational cubes.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory