This is definitely the largest 'Central Park Splendor' cultivar of Ulmus parviflora one can find. That's because cultivars were cloned from this 'mother' tree.
Legend has it that this tree was a gift from the King of Prussia, bestowed on Central Park in the 1870's. It is surprising to think that this tree is over 130 years old, but the timeline works out well; Central park was officially completed in 1873.
The cultivar was first cloned and distributed in 1989 and since has become a popular tree in parks and on streets. I speculate that a lot of 'Central Park Splendor's' thunder was stolen by the rise in popularity of Zelkova serrata in the 80's, but cannot be sure if that's really the case. From my observations, it always seems that Zelkovas are more ubiquitous than this cultivar.
The trees themselves are quite similar. They have the typical Ulmaceae asymmetrically leaf bases and small, ovate leaves with cerrated margins. Both have a vase shape and a feathery, graceful habit. Ulmus parviflora gets larger than Zelkova so perhaps the popularity of the latter can be attributed to its better use in residential lots and small spaces.
The other difference among the two is the bark. While Zelkova's bark is smooth and gray, with lenticels and, as it gets larger, exfoliated blister-like pieces of cinnamon bark, U. parviflora has a consistently exfoliated bark. Thus the common name, Lacebark Elm.
Parviflora is a popular epithet for plants; it literally means 'small flowers.' This is true, as you don't notice the diminutive blossoms of these trees.
If you want to track down this plant, it is in the lawn southwest of the 72nd Street transverse and Bethesda Fountain (i.e., due west of the bandshell).