Kenneth A. Ribet
Published 2001-05-15Version 1
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.)
Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition
The Brauer group of Kummer surfaces and torsion of elliptic curves
Mordell-Weil lattice of Inose's Elliptic $K3$ surface arising from the product of 3-isogenous elliptic curves
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