椭圆曲线 Elliptic curve
（重定向自Weierstrass equation）
在数学上，椭圆曲线（英语：Elliptic curve，缩写为EC）为一代数曲线，被下列式子所定义
，
其是无奇点的；亦即，其图形没有尖点或自相交。
若
，其中P为任一没有重根的三次或四次多项式，然后可得到一亏格1的无奇点平面曲线，其通常亦被称为椭圆曲线。更一般化地，一亏格1的代数曲线，如两个三维二次曲面相交，即称为椭圆曲线。
Weierstrass equation
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Elliptic curve 椭圆曲线
（重定向自Weierstrass equation）
![A catalog of elliptic curves. Region shown is [−3,3]2 (For a = 0 and b = 0 the function is not smooth and therefore not an elliptic curve.)](/uploads/202502/20/EllipticCurveCatalog.svg3003.png)
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form
that is non-singular; that is, its graph has no cusps or self-intersections. (When the characteristic of the coefficient field is equal to 2 or 3, the above equation is not quite general enough to comprise all non-singular cubic curves; see below for a more precise definition.)
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