An ethylene/butadiene copolymer comprising statistically distributed ethylene units butadiene units, and trans-1,2-cyclohexane units is provided. The molar fraction of ethylene units in the copolymer is greater than or equal to 50%, relative to the total number of moles of ethylene, butadiene and trans-1,2-cyclohexane units. The microstructure of the copolymer is homogeneous. A process for preparing such a copolymer and also to the uses of this copolymer, in particular in rubber compositions for tires, is also provided.