This grouping is not for just one type of rifle.  There are many variations of Remington rifles that were designed to use a sword bayonet. Which rifle used which US made sword bayonet and how many were made is the issue here. 

The similarities of the bayonets produced for the Remington, Whitney and Evans muskets are similar and absolute identification is difficult.  The associated bayonet variations listed below are only possibilities for this musket.

Bayonet Variations