On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.