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 SAGE 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 [...]
What I’m working on…
Brief, fairly technical overview of what I’ve been working on these last few months.
A less very, very stupid way of counting points on elliptic curves
Sidestepping brute-force determination of the number of points over a finite field by construction of zeta functions.
