Your serial number puts it to being made between October to December of 1891.
Just do some Googling, or as they say, "seek and ye shall find" - lots of good info out there on them. Designed for black powder cartridges - fun to load for and shoot. Before doing so - have it checked out - how is the bore, how is the chamber, is the trapdoor lock-up system tight and working, etc.
I have a Model 1884 made about the same as yours. The bore is decent with good rifling and just a few small fittings - muzzle not "funneled" from wear. However, the fellow I bought it from said there were some issues with the chamber when he and his Dad got it - some pitting that gave issues when fired with 70 grain loads of BP. They sent the barrel off to Bobby Hoyt and had the chamber re-lined which cleared up the issue in fine shape. I believe your's should have the Buffington sight.
A nice historical rifle - DO NOT use modern smokeless loads in it! If you reload - there are "some" smokeless powders that will work for it that provide lower pressures - check in the 3rd or 4th Edition of the Lyman Cast Bullet Handbooks. There is a Lee mold that duplicates one of the original style 405 grain HB bullets that gives good results in a lot of the old Tis You have to hunt for them as I believe they are made in limited runs. Usually they show up on fleabay and I have also seen them on Amazon at times
Wolf's book is an interesting read on the 45-70 TD with lots of info for duplicating the original loads - well worth the money. I purchased my copy off of the website that his widow was maintaining and copies were still available. I don't have the link handy, but it should come up if you do some Googling.
Another site to look at is Castboolits - under the black powder cartridge forum you'll find some good reading in some of the threads on 45-70 Tis.
Enjoy that trap door!