The Smith and Wesson model 13 chambered for .357 Magnum was introduced in 1974. It is a "K" frame, designating that it uses the medium size smith revolver frame. The "J" frame is smaller and the "L, N and X" frames are larger.
The 1 following the 13 indicates the first issue of the model 13 dating from it's introduction in 1974. The 13-2 was issued in 1977 with a minor change to the cylinder and the 13-3 was issued in 1982 with another minor change.
It looks about like any other revolver from that era:
The 13 is no longer available for purchase, but the model 686 is very similar:
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