| The graph method simultaneously uses the theory of quaternion algebras, elliptic curves and modular forms in order to determine all supersingular points in a given characteristic and hence to obtain a basis of S2(N). The goal of this thesis is to expose the principles of the graph method: it is therefore divided into two main parts: First, we introduce the essentials of the arithmetic of quaternions. This part is made to fit two needs: on one hand, a good introduction or novices; on the other hand, a fast and quick reference for those who are already familiar with the subject. The second part focusses on the graph method itself: after some recalls, namely about modular forms and elliptic curves, the third chapter is more specifically oriented toward the method as the last section gives a practical application of it. |
