Under the parity conjecture, an infinite family of elliptic curves of rank 2 with a torsion subgroup of order 2 or 3 is constructed.
Keunyoung Jeong. "Infinitely many elliptic curves of rank exactly two II." Proc. Japan Acad. Ser. A Math. Sci. 95 (6) 53 - 57, June 2019. https://doi.org/10.3792/pjaa.95.53