To achieve green and low-carbon electricity consumption and fully activate the user-side carbon emission potential as well as flexibility resources, an electricity-carbon collaborative trading model for multi-prosumers is constructed. The model aims to promote the utilization of distributed renewable energy by sharing energy storage capacity, thereby reduce dependence on the upper-level distribution network and fossil fuel consumption, and indirectly cutting carbon emissions. In terms of methodology, a shared operation mechanism between multi-prosumers and centralized energy storage is proposed, and a corresponding trading model is established. Its rationality and effectiveness are verified through case studies. The results show that integrating the user side into the carbon market can significantly improve the overall revenue of the electricity-carbon coupled market. Under the shared energy storage operation mode, the proportion of carbon cost drops sharply from 63.6% in the traditional mode to 0.09%. Further analysis indicates that when users' free carbon emission allowance exceeds 60%, the system can operate in a mode dominated by electricity revenue with carbon cost approaching zero. The result provides a feasible business model reference for user-side participation in the carbon market under the carbon neutrality goal.