With the continuous development of the integrated energy trading market, the issue of uncontrollable carbon emissions has become increasingly prominent. To minimize carbon emissions in the integrated energy trading market, this paper first constructs a system configuration for an electricity-heat-cooling-gas integrated energy virtual power plant, and establishes a demand conversion model and a carbon emission production priority index for it. Next, a comprehensive energy trading allocation model based on carbon emission production priority is developed. Then, based on the determined energy trading volumes, the pricing and demand response strategies for various energies are optimized with the goal of maximizing the benefits of integrated energy suppliers, shared energy storage operators, and users. Finally, the optimized energy trading strategy is compared with three other energy trading strategies, verifying its effectiveness. The research results indicate that this strategy reduces carbon emissions by 23.4%, 30.1%, and 21.1% compared to the other three strategies, respectively. While the revenue is slightly lower than that of strategies 2 and 4, the difference is around 5%, and it is even higher compared to strategy 3. This strategy effectively promotes low-carbon operation in the integrated energy trading market while also balancing economic benefits.