Modified conjugated diene copolymer, rubber compositions and tires

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The present invention provides a modified conjugated diene polymer that is prepared by polymerization of a conjugated diene compound using a catalyst containing a lanthanoid rare earth element compound in an organic solvent and then modifying the resulting polymer having an active organic metal site with a modifier, wherein the modification efficiency is not less than 15% and the cis-1, 4 bond content in the conjugated diene moiety measured by Fourier transform infrared spectroscopy satisfies the relationship (I) : [in-line-formulae]cis-1, 4 bond content≧98.00(%)  (I), [/in-line-formulae] or the modification efficiency is not less than 75% and the cis-1, 4 bond content in the conjugated diene moiety measured by Fourier transform infrared spectroscopy satisfies the relationship (II) : [in-line-formulae]94.00(%)≦cis-1, 4 bond content<98.00(%)  (II).[/in-line-formulae] The invention further provides a rubber composition containing the modified conjugated diene polymer and giving a tire exhibiting low heat build-up, satisfactory failure characteristics, and high abrasion resistance, and a tire composed of the rubber composition and exhibiting these characteristics.