*2.11. Elliptic Curves
The mathematics of elliptic curves is vast and complicated. A reasonably complete understanding of elliptic curves would require a book of comparable size as this. So we plan to be rather informal while talking about elliptic curves and about their generalizations called hyperelliptic curves. Interested readers can go through the books suggested at the end of this chapter to learn more about these curves. In this section, K stands for a field (finite or infinite) and 
the algebraic closure of K.
2.11.1. The Weierstrass Equation
An elliptic curve E over K is a plane curve defined by the polynomial equation
Equation 2.6 ...
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