Leonardo Zapponi
Published 2006-11-06Version 1
In this short note we introduce the Belyi degree of a number field K, which is the smallest degree of a dessin d'enfant having K as field of moduli. After the description of some general properties (for example, the fact that there exist finitely many number fields of bounded Belyi degree), we give a lower and an upper bound for such an invariant. We finally give some explicit examples for quadratic fields.
On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree
The set of non-squares in a number field is diophantine
Analytic curves in algebraic varieties over number fields
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