A copolymer of ethylene and a conjugated diene is provided, in which ethylene content in the copolymer is greater than 20 mol %, the copolymer has a glass transition temperature between −110° C. and −90° C., and continuous methylene sequence lengths (MSL) in the copolymer are in a range of 12-162 methylene units. A method for producing the copolymer, comprising copolymerizing ethylene and a conjugated diene in the presence of a catalyst system to obtain the copolymer is also provided, in which the catalyst system comprises a heterocyclic-fused cyclopentadienyl rare-earth metal complex, an organoboron salt compound and an organoaluminum compound, wherein the heterocyclic-fused cyclopentadienyl rare-earth metal complex is represented by the structural formula: