I managed to figure it out. The parameter can be passed using the following format:
http://www.example.com/api/endPoint?jaggedArray[0][]=406&jaggedArray[0][]=404&jaggedArray[1][]=405&jaggedArray[1][]=407
This causes a jagged array containing two arrays, each with two numbers (406 and 404 for the first, then 405 and 407 for the second,) to be received.