Exp function for Edwards curves over local fields

On isogeny classes of Edwards curves over finite fields

We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over IFq if and only if its group order is divisible by 8 if q ≡ −1 (mod 4), and 16 if q ≡ 1 (mod 4). Furthermore, ...

Isomorphism classes of Edwards curves over finite fields

Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of Fq-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski.

Ranks of elliptic curves over function fields

We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is based upon rigid and crystalline cohomology.

On Hyperelliptic Modular Curves over Function Fields

We prove that there are only finitely many modular curves of Delliptic sheaves over Fq(T ) which are hyperelliptic. In odd characteristic we give a complete classification of such curves.

Curves and Jacobians over function fields