Software Elliptic Curves and Modular Forms Number Theory
Software Elliptic Curves and Modular Forms Number Theory
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.
Top: Science: Math: Number Theory: Elliptic Curves and Modular Forms: Software
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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.
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EIS - 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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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.
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Modular Forms Software - HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.
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APECS - FTP site for Ian McConnell's MAPLE programs.
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TECC - Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
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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.
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Ellipsa - Includes Primo, an implementation of ECPP, and CPG, class polynomial builder.
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Heegner Tools - Peter Green's Heegner Points package. Requires Linux and Pari/GP 2.1.1 or higher.
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