The invention relates, in particular, to ethylene and butadiene copolymers and to a catalytic system which can be used for the synthesis of said copolymers. The inventive copolymers comprise a molar ratio of units derived from butatdiene which is greater than or equal to 8 %, said units comprising trans-1,2 cyclohexane chain formations, and have an average molecular mass Mn which is greater than or equal to 40 000 g/mol. According to the invention, the catalytic system consists of (i) an organometallic complex which is represented by either formula A or B , wherein: Ln represents a lanthanide and X represents a halogen. In formula A , two ligand molecules Cp1 and Cp2, which are each formed by a fluorenyl group, are linked to Ln. In formula B , a ligand molecule is linked to Ln, said molecule being formed by two fluorenyl groups Cp1 and Cp2 which are interconnected by a bridge P having formula MR2, wherein M is an element from column IVA and R is an alkyl with between 1 and 20 carbon atoms. The catalytic system also consists of (ii) a co-catalyst belonging to the group comprising a magnesium alkyl, a lithium alkyl, an aluminium alkyl, a Grignard reagent or a mixture of said components. Said catalytic system is such that the molar ratio (co-catalyst/organometallic complex) lies between 1 and 8.