دوره 10، شماره 2 - ( 7-1394 )
جلد 10 شماره 2 صفحات 86-77 |
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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-fa.html
URL: http://ijmsi.ir/article-1-570-fa.html
On the Elliptic Curves of the Form $y^2 = x^3 − pqx$. مجله علوم ریاضی و انفورماتیک. 1394; 10 (2) :77-86
چکیده:
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.
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