Viscosity modifier for lubricating oil and lubricating oil composition for hydraulic fluid

A viscosity modifier for lubricating oil, comprising an (C) ethylene-α-olefin copolymer having the following characteristics (C1) to (C5), and (C6):

• (C1) an ethylene molar content rate is within a range of 53 to 58 mol %,
• (C2) a rotational viscosity at 150° C. is 300 to 8,000 mPa·s,
• (C3) a Hasen chromaticity is 30 or lower,
• (C4) a molecular weight distribution (Mw/Mn) is 2.0 or more and 2.2 or less in molecular weight obtained in terms of polystyrene, as measured by gel permeation chromatography (GPC),
• (C5) a B value represented by the following formula [1] is 1.1 or more:
• B
• =
• P
• OE
• 2
• ⁢
• P
• O
• ·
• P
• E
• n
• [
• 1
• ]
• wherein in the formula [1], PE represents a molar fraction of ethylene component, Po represents a molar fraction of α-olefin component, and POE represents a molar fraction of ethylene-α-olefin chain in a total dyad chain and (C6) a weight-average molecular weight (Mw) is 20,000 to 30,000 obtained in terms of polystyrene, as measured by gel permeation chromatography (GPC).