Évènement

Elliptic curves are one of the most studied object by mathematician. They are simple enough to allow us to write down example and work with them, and co!plex enough to yield a lot of powerful theorems. Nevertheless some questions about them are hard to answer. As an example, the question « is there any elliptic curve over Q with a 11-torsion rational point » is easy to explain but tedious to answer.

Fortunately, modular curves exists. They are geometrical object who parametrizes the space of elliptic curves, and understanding them yields powerful results on elliptic curves. In my talk I’ll (try to) explain the basic definitions and how they  can be used in a practical way to answer the question above.