On the Arakelov theory of elliptic curves

 
R. de Jong

 
 
  We relate the Arakelov-Green functions of two isogenous complex elliptic curves by means of a `projection formula'. As an application of this, we calculate the Arakelov-Green function on the kernel of an isogeny. In doing so we give an answer to a question posed by Szpiro. Also we give a projection formula in the arithmetic setting.