RUBBER COMPOSITION

A rubber composition having an adhesion to a composition based on natural rubber, the composition being at least based on 5 to 95 phr of polyisoprene comprising a content by weight of 1,4-cis bonds of at least 90% of the weight of the polyisoprene; 5 to 95 phr of copolymer of ethylene and of a 1,3-diene of formula CH═CR—CH═CH, the ethylene units in the copolymer representing more than 50 mol % of the monomer units of the copolymer, the symbol R representing a hydrocarbon chain having 3 to 20 carbon atoms; and a crosslinking system. Also disclosed is a tire, in particular a tire provided with a sidewall, comprising this composition.