Article ID Journal Published Year Pages File Type
4594830 Journal of Number Theory 2010 19 Pages PDF
Abstract

In this paper we analyze the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. We show that its coordinates are rational functions on the j-invariant of the elliptic curve in characteristic p. In particular, we prove that the second coordinate is always regular at j=0 and j=1728, even when those correspond to supersingular values. A proof is given which yields a new proof for some results of Kaneko and Zagier about the modular polynomial.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory