The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 59 页 · Chapter III，Section 3「Elliptic Curves」，Definition
An elliptic curve is a pair $(E,O)$, where $E$ is a nonsingular curve of genus one and $O\in E$. (We generally denote the elliptic curve by $E$, the point $O$ being understood.) The elliptic curve $E$ is defined over $K$, written $E/K$, if $E$ is defined over $K$ as a curve and $O\in E(K)$.