Where does an S-corp that owns an LLC in another state need to file state tax returns?

I am the owner of a dual-entity corporate structure where an S-Corp registered in Alaska is the sole owner of an LLC in Oregon.  The LLC is a disregarded entity, and I am the owner of the S-corp.  In which states does the S-corp need to file a state income tax return - just Alaska, or both Alaska and Oregon?  I live in Oregon and the S-Corp has no activities in Alaska except for the fact that it is registered there.  Does the LLC, since it is a disregarded entity, have to file any tax returns on its own?