答案：E

解析：

The intersection of sets S and T is the set of integers that are in S and also in T. Set S consists of all positive integers that are multiples of 7, and set T consists of all positive integers that are multiples of 13, so the intersection of S and T is the set of positive integers that are multiples of both 7 and 13. This is the set of all positive integers that are multiples of 7*13 = 91. There are an infinite number of positive integers that are multiples of 91, so there are more than thirteen integers in the intersection of S and T.