On the Arakelov theory of elliptic curves
arXiv:math/0312359
Abstract
This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the "energy" of an isogeny between Riemann surfaces of genus 1. The latter formula provides an answer to a question originally posed by Szpiro.
arXiv comment17 pages. 2nd version; same main results as in v1, but with a section added on the average height of quotients of an elliptic curve