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Elliptic Tales by Robert Gross, Avner Ash

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Chapter 6

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TRANSITION TO ELLIPTIC CURVES

Road Map

We now can leap in, and begin to describe the objects at the heart of this book: elliptic curves. We begin by looking both backwards, repeating in brief the concepts that we need from Part I, and forwards, to explain where our journey will lead us.

 

In the first part of this book, we discussed at great length equations in two variables of the form f(x, y) = 0, where f is a polynomial of degree d > 0 with coefficients in a field K. Such an equation defines a “plane curve” C. For any field K′ that contains the field K, we can wonder about the set of all solutions of the equation when the variables ...

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