Because widely used real-world ontologies are often complex and large, one important challenge has emerged: designing tools for users to focus on sub-ontologies corresponding to their specific interests. To this end, minimal modules have been introduced to provide concise ontology views. However, computing such minimal modules remains highly time-consuming. In this paper, we design a new method combining graph and SAT techniques, to address the computation cost of minimal modules. Our approach first introduces a new abstract notion of invariant to characterize sub-ontologies sharing the same logical information. Then, we construct a finite invariant using graph representations of EL ontologies. Finally, we develop a SAT-based algorithm to compute minimal modules using this invariant. Finally, in some cases, when the computation is still too time-consuming, we provide approximations of minimal modules. Our experiments on real-world ontologies outperform the state-of-the-art algorithm. Our algorithm provides more compact approximate results than the well-known locality-based modules without losing efficiency. CCS CONCEPTS • Computing methodologies → Description logics.