Prime arithmetic Teichmüller discs in H(2

Abstract. It is well-known that Teichmüller discs that pass through “integer points ” of the moduli space of abelian differen-tials are very special: they are closed complex geodesics. How-ever, the structure of these special Teichmüller discs is mostly unexplored: their number, genus, area, cusps, etc. We prove that in genus two all translation surfaces in H(2) tiled by a prime number n> 3 of squares fall into exactly two Teichmüller discs, only one of them with elliptic points, and tha