In which case did the Supreme Court establish the "supremacy" of the federal government?

The case that established the "supremacy" of the federal government is McCulloch v. Maryland. This landmark decision, issued in 1819, held that the federal government has implied powers beyond those explicitly listed in the Constitution, emphasizing the principle of federal supremacy over state laws.

In this case, the Supreme Court ruled that the state of Maryland could not tax the Second Bank of the United States, as this would interfere with federal legislation and operations. Chief Justice John Marshall articulated that the Constitution grants Congress the power to create a national bank, and that such federal entities cannot be impeded by state actions. This established the principle that when state and federal laws conflict, federal law prevails, reinforcing the authority of the national government and ensuring a united legal framework across the states.

The other cases, while significant in their own rights, do not address the supremacy of the federal government in the same foundational manner. Brown v. Board of Education pertains to desegregation, Marbury v. Madison deals with judicial review, and Miranda v. Arizona relates to the rights of the accused.