The correct answer is C) A checklist of the equipment installed for controlling the discharge of oil. The supplement to the International Oil Pollution Prevention (IOPP) Certificate contains details on the equipment installed on the vessel for controlling the discharge of oil, as required by international regulations. This includes a list of the oil/water separating equipment, oil discharge monitoring and control systems, and other relevant pollution prevention devices. The supplement serves as a record of the vessel's compliance with MARPOL regulations for the prevention of oil pollution from ships. The other answer choices are incorrect because they do not accurately reflect the contents of the IOPP Certificate supplement. The supplement does not contain information about underwriters, permitted cargo grades, or trade routes.