Unsaturated copolymer which is a copolymer of an &agr;olefin of 2 to 12 carbon atoms and a conjugated diene monomer represented by the following formula (I-a) and has the properties: (a) in said copolymer, 1,2-addition units (including 3,4-addition units) derived from the conjugated diene monomer (I-a) form double bonds in the side chain of the copolymer, 1,4-addition units derived from the conjugated diene monomer (I-a) form double bonds in the main chain of the copolymer, and the quantity ratio of the double bonds of the side chain derived from the 1,2-addition units to the double bonds of the main chain derived from the 1,4-addition units (side chain double bonds derived from 1,2-addition units/main chain double bonds derived from 1,4-addition units) is in the range of 10/90 to 99/1 (b) five-membered rings are present in the main chain of said copolymer; and (c) the quantity ratio of the double bonds from all of the addition units to the five-membered rings (total of double bonds from all addition units/five-membered rings) is in the range of 20/80 to 90/10; wherein R2 is a hydrogen atom, an alkyl group of 1 to 8 carbon atoms or an aryl group.