## Number theory seminar in memory of F. Momose

### Momose and bielliptic modular curves

#### Ponents

Francesc Bars Cortina

#### Resum

A non-singular projective curve C of genus $\geq 2$ is named bielliptic if it admits a degree two map to an elliptic curve. Bielliptic curves over a number field have arithmetical interest because they have a non-finite number of quadratic points over some number field. The speaker began the work to list all the modular curves $X_0(N)$ which are bielliptic, and this work was extended for other classical modular curves as $X_1(N) X(N),...$ by corean mathematicians. The work of Momose on the group of automorphism for the above classical modular curves helps to complete the list of which classical modular curves are bielliptic. In the talk we will explain the main ideas and results to obtain the exact list of classical modular curves which are bielliptic and we will emphatize the points where we use the work of Momose on automorphisms groups on modular curves.

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