Section: New Results

Computation of CM class polynomials for genus 2 Jacobians

Participants : Sorina Ionica, Emmanuel Thomé [contact] .

In collaboration with Andreas Enge, Emmanuel Thomé has developed software for computing class polynomials, in the context of complex multiplication theory in genus 2. The current computations set new records which are well above the previous state of the art. A publication is in the works.

Using similar underlying tools and theory, and based on work by Sorina Ionica [15] , Sorina Ionica and Emmanuel Thomé have worked on the analysis of isogeny graphs in genus 2, when certain properties of the endomorphism ring are satisfied.