AU - Daghigh, H. AU - Didari, S. TI - On the Elliptic Curves of the Form $y^2 = x^3 − pqx$ PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 10 VI - 2 IP - 2 4099 - http://ijmsi.ir/article-1-570-en.html 4100 - http://ijmsi.ir/article-1-570-en.pdf SO - IJMSI 2 AB  - ‎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. CP - IRAN IN - LG - eng PB - IJMSI PG - 77 PT - Research paper YR - 2015