Kanonik uzamanın j-invaryantı için evrensel bir formül

In this thesis we study the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. It is proved that its Witt coordinates lie in the open affine subset of the j-line determined by the ordinary locus which implies the existence of a universal formula for the j-invariant of the canonical lifting. Canonical lifting of elliptic curves over imperfect fields are also analyzed and the notion of the canonical lifting is generalized for elliptic curves defined over bases which are not necessarily fields. The canonical lifting of the elliptic curves with some specific $j$-invariants are also explicitly computed.