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.
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