Journal of East China Normal University(Natural Sc

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On classification of isotrivial elliptic Belyi fibrations

SOORI Atif Hasan[1,2] ,DAOUSSA Daniel[1]   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. Department of Mathematics, Air University, Islamabad 44000, Pakistan
  • Received:2015-05-27 Online:2016-07-25 Published:2016-09-29


In this paper we classify relatively minimal, isotrivial families of curves $f: S \to \mathbb{P}^1$ of genus 1 with three singular fibers (Belyi fibrations). Assuming that these families have a section, we find that they are exactly 12 in number up to isomorphism. Moreover, as a result of this classification, we find that except one, the dimension of all other families in $\overline{\mathcal{M}}_1$ is zero.

Key words: elliptic fibrations, isotrivial, relatively minimal, J-invariant