Jacobians Project

A group of faculty and students at The University of Arizona have been working on the following project:

Each genus 1 curve C (defined over Q but not necessarily possessing a rational point) has associated to it an elliptic curve, namely the jacobian curve J(C). Project: Given C, determine J(C). That is to say, given C explicitly by equations defining it as the intersection of hypersurfaces in projective space, determine J(C) explicitly as a Weierstrass equation in the plane.

Other people have expressed interest and/or written related papers. In my spare time, I am continuing to work on this problem as part of my dissertation-related research.

You might be interested in our paper and related material, or in my dissertation.

Project members: You know that one of our outstanding problems is to understand the geometry of the _______ of a matrix defining a quadric. Furthermore, you know that since the low-degree cases of the project are pretty much finished, our next task is to tackle the _______ case. Attempting to access the private project material will require those two words as the account and password.