The invention relates to a triblock
polymer of formula A-B-C in which the symbol A represents a
polystyrene block, the symbol B represents a statistical
copolymer block of
ethylene and a branched 1,3-
diene of formula CH2=CR'-CH=CH2, the symbol R' represents a
hydrocarbon chain having 3 to 20 carbon atoms, and the symbol C represents a polyvinylpyridine block, the
styrene units of block A being present in the triblock
polymer in a
molar content of less than 15% of the repeating units constituting the triblock
polymer, the vinylpyridine units of block C being present in the triblock polymer in a
molar content of less than 5% of the repeating units constituting the triblock polymer, and the triblock polymer having a
Mooney viscosity ML (1+4) at 100°C greater than 30. The invention also relates to a method for synthesizing a polymer of this kind, and to a rubber composition containing same and intended to be used in particular in a tire.