Which Schedule K-1 is used to report income earned by an estate or trust?

The correct choice is Form 1041, as it is specifically designed for reporting the income, deductions, and other relevant information for estates and trusts. When an estate or trust generates income, it must file Form 1041, which is the U.S. Income Tax Return for Estates and Trusts. Accompanying this return, the estate or trust will issue Schedule K-1 (Form 1041) to report each beneficiary's share of income, deductions, and credits from the estate or trust. This information is crucial for beneficiaries as they will use it to report their share of the income on their personal tax returns.

Other forms listed in the question are not used for this purpose: Form 1120S is for S corporations, Form 8582 deals with passive activity losses and credits, and Form 1065 is filed by partnerships. Thus, Form 1041 and its associated Schedule K-1 are the appropriate options for reporting the financial activities of estates and trusts.