Provided herein are ethylene copolymers, methods for making such copolymers, and compositions made from such copolymers. The ethylene copolymers have 70 wt. % to 85 wt. % of units derived from ethylene and at least 12 wt. % of units derived from at least one α-olefin having 3 to 20 carbon atoms. The copolymers preferably further have a weight-average molecular weight (Mw) ranging from about 50,000 to about 200,000 g/mol, melting point of at least 100° C., ratio of Mw/Mn of about 1.5 to about 3.5, a content of group 4 metals of no more than 25 ppm, and a ratio of wt ppm Group 4 metals/wt ppm Group 5 metals of at least 3. Such copolymers may be particularly useful as viscosity modifiers for lubricating oil compositions.