### Modular curves and Serre's open image theorem

Heilbronn Number Theory Seminar

26th May 2021, 4:00 pm – 5:00 pm

Zoom,

Modular curves can be used to encode important arithmetic information concerning elliptic curves. These curves are defined as abstract moduli spaces and in practice it is useful to have explicit models. We will discuss a way of computing models that makes use of the arithmetic of Eisenstein series. Our application is towards a computational version of Serre’s open image theorem.

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