**Michael Stoll**

Mathematisches Institut

Universität Bayreuth

95440 Bayreuth, Germany

**Magma programs related to the paper***Torsion points on elliptic curves over number fields of small degree*

This includes the files- DKSS.magma: this contains code for verifying the computational results in the paper.
- X1_p.magma:
this contains equations for models of
*X*_{1}(*p*) for the relevant primes*p*; this file is loaded by DKSS.magma.

**Magma programs related to the paper***The Weierstrass root finder is not generally convergent*

This includes the file- Weierstrass-check.magma: this contains code to verify the results in Section 5.

**Magma program related to the paper***Irreducibility of polynomials with a large gap*

**min_red_binary_form.m**

This implements minimization and reduction for binary forms over**Q**, together with a function that tries to produce a simple form of a given morphism**P**^{1}_{Q}→*X*(by modifying by a suitable automorphism of**P**^{1}_{Q}).**Magma programs related to the paper***An application of “Selmer group Chabauty” to arithmetic dynamics*

This includes the files- SelChabDyn.magma:
this implements the algorithm described in Section 2
for curves of the form
*y*^{2}=*x*^{2g+1}+*h*(*x*)^{2}with*h*of degree at most*g*, integral coefficients and such that*h*(0) is odd and*h*(1) is even. - SelChabDyn-examples.magma: this verifies the results in Section 3.

- SelChabDyn.magma:
this implements the algorithm described in Section 2
for curves of the form
**Magma programs related to the paper***Diagonal genus 5 curves, elliptic curves over***Q**(t), and diophantine quintuples

This includes the files- diophtuples.magma: this implements the algorithm described in Section 2 (assuming GRH) for curves arising from diophantine quadruples
- diophtuples-verify.magma: this verifies the results (if feasible, without assuming GRH), given information on the elliptic curve that gives a “good” rank bound
- ellQt.magma: this implements the algorithm described in Section 5

**Computation of the Mordell-Weil group of Jacobians of genus 2**

**NOTE:**A newer (and better) version of this is now included in Magma.

This includes the files- g2wrapper.tar.gz: a compressed tarball containing all of the following files
- g2wrapper.m: the main package file
- height-new.m and myheightconstant.m: these files implement the more efficient height algorithms described in this paper
- g2wrapper.spec:
do “AttachSpec("g2wrapper.spec");” to load the code.

The main function is “MordellWeilGroupGenus2”

**Computations for the paper***The generalized Fermat equation with exponents 2, 3, n*

This includes the files- GenFermat.tar.gz: a compressed tarball containing all of the following files.
- main.magma: this loads the following four files and so verifies everything.
- section3.magma: this checks the computations in Section 3.
- section5.magma: this checks the computations in Section 5.
- section7.magma: this checks the computations in Section 7.
- section8.magma: this checks the computations in Section 8.
- verify.magma: same as section7.magma.
- localtest.magma: this contains some auxiliary functions and is loaded by section7.magma/verify.magma.
- X1_13_opt.magma: this contains some auxiliary functions and is loaded by section8.magma.

**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.