Abstract. Following Gaudry and G¨urel who extended Kedlaya’s point-counting algorithm to superelliptic curves, we introduce Harvey’s running time improvements for large enough...
In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves y3 = f(x) of genus three, over finite fields of characteristic different f...
We present an algorithm for counting points on superelliptic curves yr = f(x) over a finite field Fq of small characteristic different from r. This is an extension of an algorit...
We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural ...