Yes, it looks like a 127 or 128. That silver thing isn't original, I don't think. The bar should be curvy ahd longer. Also, the machine itself has a totally different finish than mine. The case is a Bentwood style.
Singer rearranged their site about a week ago. When you go to their site enter "serial number" in the search bar and it should take you to the identification page.
Also post your pictures under the topic Vintage Sewing Machine Shop which is Lostn51's topic. His name is Billy. There are several knowledgeable people who post there who can help you. Billy also have tutorials under that topic which will help you maintain your machine.
Good luck in getting her to work!!