ON THE FAMILY OF ELLIPTIC CURVES y2 = x3 − m2x + (pqr)2 and ARKABRATA GHOSH Mathematica, 2025 In this article, we consider a family of elliptic curves defined by E_m: y^2= x^3 -m^2 x + (pqr)^2, where m is a positive integer and p, q, r are distinct odd primes. We study the torsion as well the rank of E_m(Q).
