The rankings are prepared by the CollegeFencing360 Coaches Poll, sponsored by the United States Fencing Coaches Association and based on voting by 10 top college fencing coaches.

In January, the coaches voted for Columbia to be ranked first in the nation — all but Mr. Aufrichtig, who voted his team third best, partly to motivate his squad to earn the top honors.

“My message to them was, ‘Prove it,’ ” he said.

The team will get that chance in the Ivy League Championships this weekend at Brown University and the N.C.A.A. national championships next month.

The women’s team is also coached by Mr. Aufrichtig and is also thriving, ranked fifth in the nation with such standouts as Nzingha Prescod, a junior from Brooklyn who competed on the 2012 United States Olympic team. She is ranked first in the country and sixth in the world.

Columbia fencers practice together only twice a week, because most of them train on their own at fencing clubs in Manhattan, which is home to several clubs that have produced world-class fencers. At Columbia, the men and women practice in the same room and are assisted by two other coaches: Seoung Woo Lee, a former coach of the South Korean national team, and Akhnaten Spencer-El, who fenced on the 2000 United States Olympic team.