On the Elliptic Curves of the Form $y^2 = x^3 − pqx$

Author(s):

H. Daghigh , S. Didari

Message:
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. 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.
Keywords:

Diophantine equation , Elliptic curves , Mordell weil group , Selmer group , Birch , Swinnerton , dyer conjecture , Parity conjecture

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:10 Issue: 2, Nov 2015
Pages:
77 to 86
https://www.magiran.com/p1456648