This paper presents a general equilibrium model that explores the impact of carbon intensity on cryptocurrency pricing through two channels: (1) the portfolio choice of carbon-sensitive green investors, and (2) carbon emissions associated with cryptocurrency production. The model proposes a CAPM-like pricing relation, revealing two effects. Firstly, investors' carbon sensitivity introduces a positive carbon alpha for carbon-intensive cryptocurrencies, while carbon-neutral cryptocurrencies show no such alpha. Second, carbon intensity amplifies the systematic exposure of cryptocurrencies to the market portfolio. The theory also indicates that speculative behavior weakens carbon sensitivity, which subsequently lowers cryptocurrencies' carbon premium. Empirical evidence supports the theoretical conclusions.