Letter about component groups of elliptic curves

Abstract

This is the text of a letter written by K. Ribet to J.-F. Mestre in November, 1987. The letter proves three formulas that had been conjectured by Mestre and Oesterl\'e. These formulas concern component groups of elliptic curves that occur as optimal quotients of certain Jacobians of modular curves, and relations between the component groups and the character group of the toric component of the Jacobian. (The "toric component" and component groups are computed in positive characteristic.)