The number thirteen (13) symbolizes wholeness, unity or completion, much like seven. Jesus and the twelve disciples, Jacob or Israel and the twelve sons or tribes, the twelve zodiac and the Sun, it is clearly symbolic of the relationship between Teacher and Student.
Its negative association stems from the historical fact that the Knight's Templars were executed on Friday October 13th, 1307. Its "unlucky" aspects seem to stem from this, as all other references in the western tradition are generally positive. The Tree of Life often has either 12 or 13 limbs in many alchemical images, for example.