Section: New Results

Computation of CM Class Polynomials for Genus 2 Jacobians

Participant : 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, as Igusa class polynomials for class number above 20,000 have been computed in december 2013 using this software. An article describing this work has been accepted for publication in Experimental Mathematics [11] .

Using similar underlying tools and theory, and based on work by Sorina Ionica [13] , 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. A publication is being worked on, and is expected to be submitted in early 2014.