The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 253 页 · Chapter VIII，Section 9「The Regulator and the Conjecture of Birch and Swinnerton-Dyer」
The elliptic regulator of $E/K$ is the volume of a fundamental domain for $E(K)/E(K)_{\mathrm{tors}}$ with respect to the canonical height pairing; equivalently, for a basis $P_1,\ldots,P_r$, it is $\operatorname{Reg}(E/K)=\det(\langle P_i,P_j\rangle)$.