Below is a list of all diagonal knots of genus at most 5. The sequence of X-positions is defined so that the i-th entry indicates the position of the X (counted from the top) in the i-th column (counted from the left). Click on a grid diagram to enlarge it. 

The diagonal knots of genus at most 4 coincide with the positive braid knots of genus at most 4. The knot 13n5016 is the only positive braid knot of genus at most 5 that is not diagonal.