This paper presents parts of the engineering design process and the resulting concept for an electric engine for aviation purpose. Based on the requirement classes mentioned in [1], the concrete requirements resulting from flight operation and the approach of cooling with cryogenic gaseous hydrogen are first compiled. Then, the selected electrical concept of a 500 kW engine is presented, which serves as a basis for identifying the required components and their arrangement. Compared to conventional electric motors, additional components are required. These include hollow coils, structures to distribute the cold gaseous hydrogen to the coils and elements to support the stator laminations with the coils. Materials are then selected for these components with the aim of minimizing weight, and their geometries are predimensioned using analytical approaches and numerical methods. Finally, the individual concepts are synthesized into an overall concept. The result is a compact design for a cryogenically cooled electric motor with a power density of more than 10 kW/kg and a mass of less than 50 kg.