Elliptic curves with large torsion and positive rank over number fields   of small degree and ECM factorization
  In this paper, we present several methods for construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve factorization method (ECM). 
Andrej Dujella and Filip Najman
math.NT