- Oberwolfach references on mathematical software
- apfloat: A C++ High Performance Arbitrary Precision Arithmetic Package by Mikko Tommila
- Arageli (C++ library for computations in arithmetic, algebra, geometry, linear and integer linear programming)
- ARIBAS. This is an interactive interpreter for big integer arithmetic and multi-precision floating point arithmetic with a Pascal/Modula like syntax. ARIBAS is used for the examples of number theoretic algorithms in the book
*Algorithmische Zahlentheorie*, Otto Forster, Vieweg 1996 - BC (the exact arithmetic Unix calculator program)
- BC
- BC number theory programs (Keith Matthews)
- BCMath/PHP number theory programs (Keith Matthews)

- CALC (Keith Matthews' number theory calculator)
- Computational Laboratories in Number Theory (CLINT) (Hugh Montgomery)
- Computations on curves of genus2 and their jacobians (Paul Van Wamelen)
- Critical Strip Explorer 0.6 (Matthew Watkins and Raymond Manzoni) A Java applet which allows users to 'manually' explore the behaviour of the Riemann zeta function in and around the critical strip
- Diophantine equation solver for finding zeroes of multivariable polynomials over a prime-order field (Norman Wildberger and Michael Leeming)
- Discriminant Exponent Calculator (John Jones)
- ECPP (François Morain's elliptic curve primality-proving package)
- PRIMO, a primality proving program (Marcel Martin)
- The ECMNET Project: Find a factor of 50 digits or more by ECM
- EIS, computing Fourier coefficients of Eisenstein series attached to lattices, (M. Kuss and J. Bruinier)
- Elliptic Curve Method (ECM) factorization applet (Dario Alejandro Alpern)
- Ellpack, Maple code for simple computations with elliptic curves (Jim Carlson)
- Euclid, a C program for computing the Euclidean minimum of a number field given by a polynomial (Pierre Lezowski)
- FactInt, Advanced Methods for Factoring Integers, Version 1.5.2 (Stefan Kohl)
- Factoring software (Schulenberg and Associates Inc.)
- FLINT, Fast Library for Number Theory (William Hart and David Harvey)
- FriCAS (FriCAS is a form of Axioma and is a comprehensive computer algebra system of interest to number theorists, especially with its p-adic arithmetic component)
- GMP-ECM (Elliptic Curve Method for Integer Factorization)
- Genus 2 site (Victor Flynn)
- GNU multiple precision package (GMP)
- GL(n)pack Home Page (Kevin Broughan)
- GUESS, Maple package to guess closed form for a sequence of numbers (Bruno Gauthier)
- HECKE, A Modular Forms Calculator (William Stein)
- High Precision Arithmetic Software Directory (David Bailey)
- HYP, Mathematica package for manipulation and identification of binomial and hypergeometric series and identities (Christian Krattenthaler)
**Hypellfrob**is a C++ program/library for computing the zeta function of a hyperelliptic curve over GF(p), David Harvey- HYPERG V 1.0, Maple package devoted to symbolic computation on hypergeometric series (Bruno Gauthier)
- HYPQ, Mathematica package for manipulation and identification of q-binomial and basic hypergeometric series and identities (Christian Krattenthaler)
- IntBasis, a maple package for computing with algebraic curves (Mark van Hoeij)
- Simon Plouffe's Inverter, An online repository of mathematical constants
- JKL-ECM: An implementation of ECM using Hessian Curves, by Henriette Heer, Gary McGuire, Oisin Robinson
- KANT (Michael Pohst: Technisches Universität Berlin)
- LiDIA
- Implementations of extended LLL, by Wilberd van der Kallen
- MAGMA (John Cannon: University of Sydney)
- MAGMA Calculator
- +Ideals, A package for ideal arithmetic in number fields (Jordi Guàrdia, Jesús Montes & Enric Nart)
- MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied (Szabolcs Tengely)

- MegaNumberS (Chris Harrison)
- MPFR (Paul Zimmermann)
- Multidigit multiplication for mathematicians (Dan Bernstein (dvi 87K))
- MuPAD
- MWRANK, a program for finding the rank of an elliptic curve over the rationals (John Cremona)
- NTL: A Library for doing Number Theory (Victor Shoup)
- NTRU Cryptography
- NZMATH, a Python based number theory oriented calculation system
- p-adic Arithmetic (Stany De Smedt)
- PARI:
- PARI/GP
- Pari-Gp routines for number theory (Fernando Rodriguez Villegas)
- Computing special values of L-functions (ComputeL - a PARI package by Tim Dokchitser)
- Pari-tty Userinterface for Pari-GP (Windows XP) (Gottfried Helms)
- Pari scripts on Tate Pairing Computation via Elliptic Nets, Elliptic Divisibility Sequences Tools and Elliptic Nets Tools, Katherine Stange
- Number Theory and PARI (David J. Wright)

- Periods of Hilbert modular forms and rational points on elliptic curves, Adam Logan and Henri Darmon
- Peter Green's Heegner Points Package
- PIPS: Polynomials over Galois Fields, A calculator program by Florent Chabaud
- Primo, a primality proving program based on the ECPP algorithm (Marcel Martin)
- SageMath (formerly Sage), the Sage Mathematics Software System (William Stein et al.)
- Ken Ribet talks about his experiences with Sage
- Sage Days 16: CRM Barcelona, Spain - Computational Number Theory, June 22-27, 2009 (transcripts and videos of talks)

- Programs (Ratpoints, J-points), Ratpoints finds rational points on hyperelliptic curves, J-points searches for rational points on the Jacobian of a genus 2 curve (Michael Stoll)
- SHARK : computing Tate-Shafarevich groups via Iwasawa theory (Christian Wuthrich)
- SIMATH (development discontinued)
- SymPy module on diophantine equations
- Number Theory Programs for the TI-92 (Paul Pollack)
- Implementation of sum of three palindromes algorithm (Lewis Baxter)
- UBASIC 8.8e (Yuji Kida) A basic interpreter with fast multiprecision arithmetic
- WIMS: an online calculator program by Xiao Gang
- Computes the continued fraction expansion of a real number (The convergents are not accurate, but the partial quotients seem to be correct)
- Test Goldbach's conjecture with Factoris
- Factors expressions

- XR-exact real arithmetic package (Keith Briggs)

- The On-Line Encyclopedia of Integer Sequences (OEIS)
- LMFDB (a database of L-functions, modular forms, and related objects)
- The Third Edition of the Cunningham Book (note: the link to the online book Cont. Math.
**22**is broken) - The 310,716 elliptic curves of prime conductor less than 10
^{8 }(Oisin McGuinness) - manYPoints - Table of Curves with Many Points
- Iwasawa invariants of elliptic curves (Robert Pollack)
- Database of Automorphic L-functions (Stephen Miller)
- The Cunningham project
- Data on Mordell's curve y
^{2}=x^{3}+k (Michael Bennett) - Noam Elkies' computational number theory page (eg congruent numbers tables)
- A Database for Number Fields (Jürgen Klüners and Gunter Malle)
- Tables of Fermat near-misses (Noam Elkies)
- Tables related to Marshall Hall's conjecture (Noam Elkies)
- Tables of vanishing Fermat quotients, R. Ernvall and T. Metsänkylä, 1995
- High rank elliptic curves with prescribed torsion (Andrej Dujella)
- Tables of Dedekind zeta functions at negative integers (Eyal Goren)
- Tables of zeros of the zeta function (Andrew Odlyzko)
- John Cremona's Elliptic Curve Data
- Online version of John Cremona's elliptic curve tables
- Number fields of low degree : (John Jones, Arizona State University)
- Classical Modular Polynomials (Michael Rubinstein)
- Modular forms database (William Stein)
- Mathematical constants and computation (Xavier Gourdon and Pascal Sebah)
- Tables of imaginary quadratic fields with small class number
- Tables of ideal classs groups of real quadratic fields (Michiyo Saito and Hideo Wada)
- New Modular Hyperelliptic Curves (E. González-Jiménez)
- New modular non-hyperelliptic genus 3 curves (Enrique González Jiménez)
- Genus 2 curves with modular jacobians (E. González-Jiménez)

Return to Number Theory Web page

* Last modified 22nd February 2019*