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Elliptic curve

an algebraic curve of genus 1 equipped with a basepoint
A catalog of elliptic curves. Region shown is [−3,3]2 (For (a, b) = (0, 0) the function is not smooth and therefore not an elliptic curve.)

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form

which is non-singular; that is, the curve has no cusps or self-intersections. Formally, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O.


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