Classification of the rank of a certain family of elliptic curves

Richa Sharma, Bidisha Roy, Arkabrata Ghosh

In this article, we study the family of elliptic curves $E_{-2pq}:y^2=x^3-2pqx$, where $p$ and $q$ are distinct odd primes. Using a $2$-isogeny methods and some elementary techniq…