Final answer:
Ole Miss won its first conference crown under Coach Tom Swayze in 1959, marking the beginning of a successful period in the university's baseball history.
Step-by-step explanation:
Ole Miss claimed its first of four conference crowns under Coach Tom Swayze in the year 1959. Swayze was a notable figure in the history of Ole Miss baseball, and under his leadership, the team achieved significant success. The university's baseball history is rich with accomplishments, with Swayze's era being particularly notable for setting a strong foundation for the program's future successes.