For questions regarding elliptic curves. Questions on ellipses should be tagged [conic-sections] instead.

An elliptic curve is a smooth, non-singular projective curve of genus $1$ with a specified point $\mathcal{O}$. It forms a abelian group under point addition. It is an object of much study in number theory.

Elliptic curves are not to be confused with ellipses. Questions on ellipses should be tagged .

More informally, elliptic curves are cubic curves that have a shape that looks like a donut.

An elliptic curve can be defined by an equation of the form

\begin{equation*} y^2=x^3+ax+b \end{equation*}

and this is non-singular, ie, its graph has no cusps or intersections. They can be defined over any field $K.$

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