The present invention relates to an elastomer mixture resulting from the modification of a diene elastomer by a coupling agent that introduces, into the elastomer chain, an alkoxysilane group bearing a tertiary or secondary amine functional group. This mixture predominantly comprises the diene elastomer coupled by the alkoxysilane group bearing a tertiary or secondary amine functional group which is bonded to the diene elastomer through the silicon atom. The invention also relates to a reinforced rubber composition, in particular that can be used for the manufacture of tires, which comprises a reinforcing filler and an elastomer matrix comprising at least this elastomer mixture, and to its preparation process. This composition has improved hysteresis and mechanical properties in the vulcanized state, and also improved processing in the uncured state.