The large, three-headed muscle that is the prime extensor of the forearm at the elbow joint is the

"triceps brachii muscle"

The  triceps brachii muscle is a muscle that has three heads, as its name indicates, and can be found in the posterior surface of the arm. This muscle function is to extend the forearm at the elbow joint being an antagonist of the biceps brachii and brachialis muscles that flexes the forearm at the elbow joint.