Séminaire Combinatoire et Théorie des Nombres ICJ

# Bielliptic curves

## by Francesc Bars (Universitat Autònoma de Barcelona)

Europe/Paris
Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

### Bât. Braconnier, salle Fokko du Cloux

#### ICJ, Université Lyon 1

Description

First, we introduce bielliptic curves $C$ over a number field $K$ and the relation with non-finiteness of quadratic points (running all quadratic field extension over $K$) for $C$. Next, we observe for a fixed non-bielliptic smooth plane curve a consequence on quadratic points (in particular for Fermat equation). The main part of the talk we will discuss on biellipticity for the modular curves $X_0^*(N)$. This is a joint work with Prof. Josep González Rovira.