Some families of supersingular Artin-Schreier curves in characteristic >   2
  In this short paper we prove that the following two 1-dimensional families of Artin-Schreier curves are supersingular: y^7 - y = x^5 + c.x^2 over F_7 y^5 - y = x^7 + c.x over F_5 (for some parameter c). Our method is developed upon the p-adic Dwork's method. 
Hui June Zhu