The calculation of properties of elliptic curves such as their torsion groups, rank, and point counting on elliptic curves over finite fields is a highly non-trivial process. This category lists software programs written specifically to perform these calc...
This page was last updated on August 27th, 2008
This page was last updated on August 27th, 2008
Software (from Elliptic Curves and Modular Forms)
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TECC
Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
The CAGE Project
Classes for Algebraic Geometry and Ellliptic Curves, implemented in C++.
MWRANK
Mordell-Weil rank of elliptic curves over the rationals, by John Cremona.
Code to Compute Heights on Elliptic Curves
Magma implementation of Silverman's algorithm to compute the canonical height on an elliptic curve over a number field or function field, by Martine Girard.
Modular Forms Software
HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.
Heegner Tools
Peter Green's Heegner Points package. Requires Linux and Pari/GP 2.1.1 or higher.
APECS
FTP site for Ian McConnell's MAPLE programs.
Ellipsa
Includes Primo, an implementation of ECPP, and CPG, class polynomial builder.
Periods of Hilbert Modular Forms
A package of PARI programs (v.2.1.1 or higher) for calculations described in "Periods of Hilbert modular forms and rational points on elliptic curves" by H. Darmon and A. Logan.
Modular Quaternion Groups
Fundamental domains for Shimura curves, written in GAP. Documented with description of algorithms used and program structure, input and output. Results for quaternion algebras with discriminant up to 100.
EIS
Software for computing Fourier coefficients of Eisenstein series attached to lattices by M. Kuss and J. Bruinier. Binaries for x86-Linux.
Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
Classes for Algebraic Geometry and Ellliptic Curves, implemented in C++.
Mordell-Weil rank of elliptic curves over the rationals, by John Cremona.
Magma implementation of Silverman's algorithm to compute the canonical height on an elliptic curve over a number field or function field, by Martine Girard.
HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.
Peter Green's Heegner Points package. Requires Linux and Pari/GP 2.1.1 or higher.
FTP site for Ian McConnell's MAPLE programs.
Includes Primo, an implementation of ECPP, and CPG, class polynomial builder.
A package of PARI programs (v.2.1.1 or higher) for calculations described in "Periods of Hilbert modular forms and rational points on elliptic curves" by H. Darmon and A. Logan.
Fundamental domains for Shimura curves, written in GAP. Documented with description of algorithms used and program structure, input and output. Results for quaternion algebras with discriminant up to 100.
Software for computing Fourier coefficients of Eisenstein series attached to lattices by M. Kuss and J. Bruinier. Binaries for x86-Linux.
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