Random copolymer (I) of ethylene, an alpha -olefin and a branched conjugated polyene has the following properties : (i) 0 ethylene 100 mole-%; 0 alpha -olefin 100 mole-%; and 0 iodine (I2) number 370 g/100 g; (ii) 0.1 intrinsic viscosity ( epsilon ) 10 dl/g, measured in decalin at 135 deg C; and (iii) the molecular weight distribution (ratio of weight average molecular weight Mw to number average molecular weight Mn) /3 5. Also claimed are: (1) copolymer compositions containing (I); (2) cross-linkable copolymer compositions containing (I) and cross-linking agent(s); and (3) methods of producing (I).