85 search results - page 2 / 17 » Factorization with genus 2 curves |
MICS
2010
13 years 4 months ago
2010
In the early 1990s, Flynn gave an explicit description of the Jacobian of a genus 2 hyperelliptic curve to perform efficient arithmetic on these objects. In this paper, we give a ...
ANTS
2010
Springer
13 years 9 months ago
2010
Springer
![Visualizing Elements of Sha[3] in Genus 2 Jacobians](https://www.sciweavers.org/files/imagecache/thumbnail/default/content.jpg "Visualizing Elements of Sha[3] in Genus 2 Jacobians")
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
MOC
2000
13 years 5 months ago
2000
We describe a method for proving that two explicitly given genus two curves have isogenous jacobians. We apply the method to the list of genus 2 curves with good reduction away fro...
PAIRING
2007
Springer
13 years 12 months ago
2007
Springer
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. ...
ANTS
2000
Springer
13 years 10 months ago
2000
Springer
We shall discuss the idea of finding all rational points on a curve C by first finding an associated collection of curves whose rational points cover those of C. This classical ...