Here is an official link to the information that COP filed with the IRS. It includes the official IRS form that you will need to compute your tax basis. I suggest that you print a copy of this IRS form and keep it for your tax records. Here is the link:
If you do not have them in a brokerage account it would be wise to have them there. There are so many reasons, such as selling and buying, you will get statements indicating the action, and the list can go on and on. There is usually a minimum amount but you already have shares there. If you do not want the broker to lend out your shares: To avoid using securities as collateral, instruct the broker-dealer to open a cash account only.