%0 Journal Article
%A Daghigh, H.
%A Didari, S.
%T On the Elliptic Curves of the Form $y^2 = x^3 − pqx$
%J Iranian Journal of Mathematical Sciences and Informatics
%V 10
%N 2
%U http://ijmsi.ir/article-1-570-en.html
%R 10.7508/ijmsi.2015.02.008
%D 2015
%K Diophantine equation, Elliptic curves, Mordell weil group, Selmer group, Birch and Swinnerton- dyer conjecture, Parity conjecture.,
%X 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.
%> http://ijmsi.ir/article-1-570-en.pdf
%P 77-86
%& 77
%!
%9 Research paper
%L A-10-739-1
%+ University of Kashan
%G eng
%@ 1735-4463
%[ 2015