Volume 10, Issue 2 (10-2015)                   IJMSI 2015, 10(2): 77-86 | Back to browse issues page

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Daghigh H, Didari S. On the Elliptic Curves of the Form $y^2 = x^3 − pqx$. IJMSI 2015; 10 (2) :77-86
URL: http://ijmsi.ir/article-1-570-en.html

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel and Sierpinski is true.

Type of Study: Research paper | Subject: Special

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