Elephant Butte is the distinct rocky high point to the NW of the Alderfer/Three Sisters western parking area. At Bluebird Meadows is dominates the NW skyline.
Elephant Butte is a Denver Mountain Park, and it seems there are no signs or marked trails, though you can find a fairly good trail along the east face. The views from the summit are amazing and there is a lot of exposed rock. Reportedly you can access the summit from the west, but I have no first hand information on that access.
Park at Bluebird Meadows (Alderfer/Three Sisters western lot) and take the Mountain Muhly Trail north to the NE ridge of Elephant Butte. Follow the ridge, bearing slightly left (south) and you might pick up the east face trail. If you lose it, then you'll have to find a path up the 3rd/4th class slabs to the summit. Then it's not too hard to find a path down to the south and then contour back around to the north on the east face trail.