Endomorphisms of Elliptic Curves
The isomorphism classification of elliptic curves was carried out completely in terms of the Weierstrass equation with a minimum of algebraic geometry. This was possible because an isomorphism between two curves with equation in normal form is given by simple formulas. The situation with homorphisms is not so easy and more algebraic geometry is needed. The exception to this is multiplication by 2 and the 2-isogeny, see 4(5.2).
KeywordsElliptic Curve Elliptic Curf Galois Group Abelian Variety Complex Torus
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