Copolymer, lubricating oil viscosity modifier, and lubricating oil composition

A method of improving low-temperature properties of a lubricating oil composition by adding a copolymer to a lubricant oil base stock, wherein the copolymer containing a constituent unit derived from ethylene, and a constituent unit derived from an α-olefin having 3 to 20 carbon atoms, the copolymer having the following (1) to (6):

• (1) the copolymer has a melting point (Tm) measured by DSC of −20° C. to 100° C.;
• (2) the copolymer has a molecular weight distribution (Mw/Mn) measured by GPC of 1.6 to 5.0;
• (3) the copolymer has a half-width (ΔThalf) of a melting peak measured by DSC of 90° C. or less;
• (4) the half-width (ΔThalf) and the melting point (Tm) satisfy the relationship shown by the expression:
• ΔThalf≦−0.71×Tm+101.4
• (5) the copolymer has a heat of melting (OH) measured by DSC of 100 J/g or less;
• and
• (6) the heat of melting (ΔH), the crystallization temperature Tc measured by DSC, and the crystallization temperature Tcrystaf measured by a CRYSTAF method satisfy the relationship shown by the expression:
• Tc−Tcrystaf≧0.028×ΔH+25.3
• wherein the amount of the copolymer is 0.1 to 30 percent by weight based on the lubricant oil composition.