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Context. NOAA AR 10501 produced three flares on 2003 November 18. Two of them were associated with coronal mass ejections (CMEs). Aims. We model the magnetic-field structure of the active region, study the magnetic-topology evolution, and propose a scenario of the observed events. Methods. The coronal magnetic field is reconstructed using a topological model (also called magnetic-charge model). We present an automatic method of choosing the magnetic charges for the case where the charges are located beneath the photosphere. The new method improves quantitative analysis of magnetograms and makes processing faster. Results. We demonstrate that coronal conditions became more favourable for magnetic reconnection before the flaring events. It is also shown that the magnetic-field configuration at the time of both CMEs was critical, close to what is called "topological trigger". We assume that the topological trigger played a key role in the initiation of these CMEs.