I am quite sure I got the dreaded Corolla oil consumption issue for the 2001 model. I put in about quart and a half every 1000 miles, seems worse in winter. I noticed some black carbon on the tail pipe, not greasy just carbon. Is this a sign it burns oil? Can't find any leak underneath, dry as a bone. 120,000 miles on it, own for one year and reliable except for oil consumption.