THE GENUS OF THE ENDOMORPHISMS OF A SUPERSINGULAR ELLIPTIC CURVE

摘要

We describe the genus of the quadratic space Hom(E', B) of homomor-phisnis of two aupersingular elliptic curves E and E' and .study the map (E',E) i-> Houi(J5', E) from the set of pairs of supersingular elliptic curves over Wp to the set of proper classes hi this genus. We show that this map is surjective and determine its fibres. In the last section we use the Minkowski-Siegel formula to express the mean value of the representation of a ternary quadratic form in this genus by local representation densities.