# Finding a rational point on the elliptic curve \(y^2 = x^3 + 7823\)

## Jennifer S. Balakrishnan

An elliptic curve E can be thought of as a smooth curve of the form

together with a special point \(O\) ‘at infinity’. Suppose we fix integers \(A,B\). The set of solutions in rational numbers to \((*)\), together with \(O\), has the structure of an abelian group, and understanding this group \(E(Q)\) has led to many interesting developments in number theory.

I’ll give an overview of the theory of ellipticcurves over the rationals, say a little about a million-dollar problem involving elliptic curves, and tell you about finding a rational point on the curve

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