# On the elliptic curves of the form $y^2=x^3-3px$

Document Type : Research Paper

Authors

University of Kashan

Abstract

By the Mordell-Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎There is no known algorithm for finding the rank of this group‎. ‎This paper computes the rank of the family $E_p:y^2=x^3-3px$ of elliptic curves‎, ‎where p is a prime‎.

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### History

• Receive Date: 29 April 2013
• Revise Date: 25 August 2013
• Accept Date: 25 August 2013