Class years are almost always mentioned alongside alumni names—see names of people for guidelines in that context and punctuation section for apostrophe guidelines.
When mentioned in the context of a specific class, treat the phrase as a capitalized proper noun.
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As the 2019 Convocation speaker, Bill Nye '77 will inspire the Cornell Class of 2019 to be curious, informed, hopeful agents of change.
See Names of people section for more variations.