Solar flares are spectacular coronal events that release large amounts of energy. They are classified as either eruptive or confined(1,2), depending on whether they are associated with a coronal mass ejection. Two types of model have been developed to identify the mechanism that triggers confined flares, although it has hitherto not been possible to decide between them because the magnetic field at the origin of the flares could not be determined with the required accuracy(3-8). In the first type of model, the triggering is related to the topological complexity of the flaring structure, which implies the presence of magnetically singular surfaces(9-11). This picture is observationally supported by the fact that radiative emission occurs near these features in many flaring regions(12-17). The second type of model attributes a key role to the formation of a twisted flux rope, which becomes unstable. Its plausibility is supported by simulations(18-22), by interpretations of some observations(23,24) and by laboratory experiments(25). Here we report modelling of a confined event that uses the measured photospheric magnetic field as input. We first use a static model to compute the slowly evolving magnetic state of the corona before the eruption, and then use a dynamical model to determine the evolution during the eruption itself. We find that a magnetic flux rope must be present throughout the entire event to match the field measurements. This rope evolves slowly before saturating and suddenly erupting. Its energy is insufficient to break through the overlying field, whose lines form a confining cage, but its twist is large enough to trigger a kink instability, leading to the confined flare, as previously suggested(18,19). Topology is not the main cause of the flare, but it traces out the locations of the X-ray emission. We show that a weaker magnetic cage would have produced a more energetic eruption with a coronal mass ejection, associated with a predicted energy upper bound for a given region.