Number theory computer programs

Peter Green's Heegner point package

A package of PARI routines to compute Heegner points over ring class fields of imaginary quadratic fields and Stark-Heegner points over ring class fields of real quadratic fields, as explained in the article
H. Darmon and P. Green. Elliptic curves and class fields of real quadratic fields: algorithms and evidence. Experimental Mathematics 11:1 (2002) 37-55.

Derived periods and the Mazur-Tate circle pairing

A collection of PARI routines to compute the Mazur-Tate circle pairing, derived periods, and test a variant of the Birch and Swinnerton-Dyer conjecture for the Mazur-Tate circle pairing. These routines were used to gather the numerical data in
M. Bertolini and H. Darmon. A Birch and Swinnerton-Dyer conjecture for the Mazur-Tate circle pairing. Duke Math Journal 122 (2004) 181-204.

Adam Logan's package for computing periods of Hilbert modular forms
and rational points on elliptic curves

This is the software that was used in performing the calculations that are summarised in
H. Darmon and A. Logan. Periods of Hilbert modular forms and rational points on elliptic curves. IMRN, 40 (2003) 2153-2180.

Stark-Heegner points via overconvergent modular symbols

A collection of Magma programs for computing Stark-Heegner points. The approach that is followed represents a significant improvement over the one which is documented in the earlier article
H. Darmon and P. Green. Elliptic curves and class fields of real quadratic fields: algorithms and evidence. Experimental Mathematics 11:1 (2002) 37-55.

The improved algorithm, based on the notion of overconvergent modular symbols introduced by Stevens and Pollack, is explained in the article
H. Darmon and R. Pollack. The efficient calculation of Stark-Heegner points via overconvergent modular symbols.

Antoine Gournay's Heegner points package

A collection of Pari programs writtenn by Antoine Gournay to do the Heegner point calculations that appear in his McGill Masters thesis.

Iterated integrals and rational points

A collection of SAGE programs written by Sam Lichtenstein and Mike Daub, to compute rational points on elliptic curves arising from certain algebraic cycles on a product of modular curves, following this paper from a project at the Arizona Winter School on Stark-Heegner points.