Abstract:I: We present a general numerical method for computing Belyi maps that employs their relationship with triangle groups, permutation triples, and dessins d'enfants. Using this method, we have computed an exhaustive database of Belyi maps in low degree, which is accessible both as a Magma package, and on the web as a part of the L-functions and modular forms database (LMFDB). We showcase some features of the database both in Magma and on the LMFDB website

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