I had to do some digging for this:
Not a hop Hornbeam fruit is not correct, lower side of leaf will be hairy (can't tell from here)
Definately an elm: leaves with 6-20 main nerves on each side of midrib (yes), the lowest pair above the base of the blade, all the nerves at nearly the same angle parallel to one another (yes); margins of leaves toothed rather regularly from base to summit (yes), branches with solid pith, fruit dry, either a flat winged fruit (samara) (yes) or wingless bur-like nut, ripening and falling before June (yes)
Hold the leaf between thumb & finger, slide back and forth. If it is real sticky in one direction from the "hairs" on the topside, it's probably a "slippery elm", Ulmus rubra: bud scales conspicuously covered with dense orange-brown or rusty-colored hairs; inner bark slippery when chewed.
Otherwise: I vote for siberian elm, Ulmus pumila: leaves nearly equal-sided at the base; margins of leaves simply toothed (without any break or cut on each tooth); lower surface of leaves glabrous [without hairs]; flowers nearly without stalks (sessile), not drooping; margins of fruits without hairs projecting (Looks like it to me!)
The presence of the tree in a residential yard, filled with water suggests Siberian elm, right off the bat, since they are notorious for that.
Another possibility: American (white) elm: Ulmus Americana: None of the branches developing corky wings or woody outgrowths (yes); flowers occuring in clusters or groups, their stalks originating from the same point (yes); fruits glabrous [without hairs] on the side which covers the seed; flowers with long stalks, soon drooping; lower surface of leaves hairy or becoming glabrous.
Slippery and American elms have rather large leaves, Siberians have the smallest. If I could see the tree in person, they are all easy to tell apart with a glance at the bark & leaves. Not so easy from pictures.