Regulator of a number field[r]: The discriminant of the logarithmic embedding of the generators of the unit group of the maximal order of an algebraic number field. [e]
Regulator of an elliptic curve[r]: The determinant of the height pairing on a generating set for the Mordell–Weil group of an elliptic curve. [e]
Financial regulator[r]: The United States Securities and Exchange Commission gives as its mission "to protect investors, maintain fair, orderly, and efficient markets, and facilitate capital formation". Financial regulators in other countries have similar responsibilities. [e]