It cannot be a beech or an elm. Birch is a good candidate, although I am not familiar with all the trees that grown down your way.
The irregular number of jags that accompany each large tooth is common in birch, although also common with many other tree leaves. Bark that peels across the trunk rather than lengthwise up and down also points to birch. Thanks for giving all the description you can, every little factoid helps.
If it is a birch, you should easily see lenticels on the twigs and branches. These are raised parts on the bark that vary from looking like numerous grayish dots on small brown twigs, that lengthen across the branch (not lengthwise on the branch) as the twig/branch ages.
Multiple trunks are common in landscaped birches. As the bark ages, bark should go from fuzzy on the twig ends (1-6 inches), to smooth (with raised lenticels), to peeling, and finally to rough and furrowed (when the trunk is a foot in diameter or more). Exactly when these transitions occur is very variable and depends on size, age, genetics, and where the tree lives. The important observation is that the transitions go in stated succession. Winter leaf buds should be very pointy. Fall color yellow (although many many trees have yellow fall color).
