There are only three reasons for no eggs and no egg shells left in the nest.

A predator such as a raccoon or other predators ate the eggs (all parts of them) after accessing the nest.

The second reason would be something wrong with the eggs and the swans dumped them out of the nest into the water and another predator such as a turtle took them. Turtles, foxes, raccoons, minks, opossums, etc., are good candidates for eggs as a food source.

Finally, the last reason would be human. In many states, Mute Swans are being eradicated due to baseless reasons other than the purpose of removing them so that the larger Trumpeter Swans can be introduced into an area for Trophy Waterfowl hunting purposes. “Volunteers” from USDA Wildlife Services or state wildlife entities oil or addle eggs, smash them after taking them from the nest, killing the adults and even stomping the young to death. If this is the case with your swans, then they are extremely lucky to still be alive. The only other reason that a human would want the eggs would be to try and incubate the eggs and start their own flock without having to pay for them. The Regal Swan