Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4594830 | Journal of Number Theory | 2010 | 19 Pages |
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