**Michael Stoll**

Mathematisches Institut

Universität Bayreuth

95440 Bayreuth, Germany

**Data related to Kummer varieties of hyperelliptic Jacobians of genus 3**

This includes the files- Kum3.tar.gz: a compressed tarball containing all of the following files (about 900 kB)
- Kum3-quartics.magma: the quartics defining the Kummer variety
- Kum3-invariants.magma:
the quartics that are invariant under the action of
*J*[2] - Kum3-deltas.magma: the quartics giving the duplication map
- Kum3-biquforms.magma: the bi-quadratic forms giving the add-and-subtract morphism
- Kum3-Xipols.magma: expressions for the products of the coordinates with Ξ
- Kum3-torsionmats.magma: the matrices giving the action of the 2-torsion points
- Kum3-verification.magma: a script that verifies a number of computational claims in the paper
- G3Hyp.spec, G3Hyp.m, G3HypHelp.m: package files providing code for various tasks; do “AttachSpec("G3Hyp.spec");”

**ratcycles.magma**

This demonstrates how to determine the set of rational*n*-cycles under*z*↦*z*^{2}+*c*for*n*= 1,2,3,4,5. (Following Flynn, Poonen and Schaefer.)**kleinquartic.magma**

This shows how to determine the set of rational points on the Klein Quartic*x*^{3}*y*+*y*^{3}*z*+*z*^{3}*x*= 0. (Idea stolen from Nils Bruin.)**ellchab.magma**

This shows how to determine the set of rational points on*y*^{2}=*x*^{6}+*x*^{2}+ 1 using “elliptic curve Chabauty”. (Example from Joe Wetherell's thesis, method by Nils Bruin.)**g2ff.magma**

This demonstrates how you can work with genus 2 curves over function fields.**Xdyn06.magma**

This is the file providing the computational details for the paper

M. Stoll:*Rational 6-cycles under iteration of quadratic polynomials,*London Math. Soc. J. Comput. Math.**11**, 367-380 (2008).**preimages.magma**

This is the file providing the computational details for the paper

X. Faber, B. Hutz and M. Stoll:*On the number of rational iterated pre-images of the origin under quadratic dynamical systems,*Int. J. Number Theory**7**:7, 1781-1806 (2011).**chabauty-MWS.m**

This is an implementation of the "Chabauty + Mordell-Weil Sieve" approach to find all rational points on a genus 2 curve over**Q**whose Jacobian has Mordell-Weil rank 1.

Just do “Attach("chabauty-MWS.m");” have a look at the example at the beginning of the file to see how to use it.

(This is now contained in Magma.)**MWSieve-new.m**

Here is an implementation of the Mordell-Weil Sieve that can be used to verify that a given curve (of genus 2 over**Q**) does not have rational points, see

N. Bruin, M. Stoll:*The Mordell-Weil Sieve: Proving non-existence of rational points on curves,*LMS J. Comput. Math.**13**, 272-306 (2010).

See the beginning of the file for how to use it.