I’ve been trying to extend the results of the work described in the previous post, and following a suggestion of Noam Elkies have changed my search strategy from points corresponding to simple EDS triples to those given by (A,u,c) parametrisations as described here. Experimenting with these revealed some serious deficiencies with the height function in [...]
Archive of posts filed under the Algebraic Geometry category.
Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
I have uploaded a preprint of my third paper to the arXiv. In a break from my cyclotomic matrix work, this revisits a project I first became interested in over four years ago: the search for points with small height on elliptic curves over number fields, through the use of elliptic divisibility sequences. There used [...]
Geometry Club Talk: Computational aspects of ECDLP
Notes from my geometry club talk given April 18th, 2008.
First Year Presentation
Slides and Report from my first year presentation on the point counting problem.
Geometry Club Talk: Hyperelliptic curves
Slides from my talk on the geometry of hyperelliptic curves in connection with cryptography.
Genus 2 jacobian group law in Maple
Maple procedures for working with the group of rational divisors of a genus 2 hyperelliptic curve; designed for compatibility with generic_group procedures.
Computation in the jacobian of hyperelliptic curves
Polynomial representation of divisors and the notion of rationality.
From points to divisors: the jacobian.
Extending the idea of the group of rational points of an elliptic curve to higher genus: the jacobian of a hyperelliptic curve.
Elliptic Curve group law in Maple
Maple procedures for working with the group of rational points of an elliptic curve; designed for compatibility with generic_group procedures.
Baby Steps, Giant Steps, and element orders
Establishing the order of an element by BSGS.
