Software Elliptic Curves and Modular Forms Number Theory

Software

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 calculations.

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• - 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.
  
• - 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.
  
• - Includes Primo, an implementation of ECPP, and CPG, class polynomial builder.
  
• - 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.
  
• - Mordell-Weil rank of elliptic curves over the rationals, by John Cremona.
  
• - Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
  
• - FTP site for Ian McConnell's MAPLE programs.
  
  

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