Apparaît dans la collection : COUNT - Computations and their Uses in Number Theory / Les calculs et leurs utilisations en théorie des nombres
In this talk we will see that there are only finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater than or equal to 19, no such curve exists. For modular curves of Shimura type we will show that none can admit a smooth plane model of degree 5, 6 or 7. Further, if a modular curve of Shimura type admits a smooth plane model of degree 8 we will see that it must be a twist of one of four curves.
This is joint work with Samuele Anni and Eran Assaf.