The rifle only has Model 700 stamped on it. It has a 24" barrel. I have no clue how to determine twist rate.
As far as I know, all factory Reminton's in .260 were produced with a 1 in 9" twist.
As to being a "coyote" gun - far from it. The .260 is one of the most versitile calibers ever made. It is suitable for anything from predators all the way up to elk (elk within reason). For deer sized game it is ideal.