Number theory calculator sites/tables

• 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
• 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)
• Generic two integer variable equation solver (Dario Alejandro Alpern) (sometimes gives solutions belonging to the same family)
• 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)
• Math-Prime-Util (Dana Jacobsen)
• MegaNumberS (Chris Harrison)
• Metanumbers (Jessy Metaxas)
• 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)
• 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)
• 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 (1951-2014) Also Chen Xin obituary and Notices of the AMS article on WIMS
  • 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
  • Factors expressions
• Wolfram Alpha (computes continued fractions amonst other things)
• XR-exact real arithmetic package (Keith Briggs)

Number Theory Tables

• The On-Line Encyclopedia of Integer Sequences (OEIS)
• LMFDB (a database of L-functions, modular forms, and related objects)
• Data associated with a paper of Benjamin Matschke and Rafael Känel
• 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 10⁸ (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 y²=x³+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)
• On the p-divisibility of 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 (Andrew Sutherland)
• Weber modular polynomials (Andrew Sutherland)
• Partition class polynomials (Andrew Sutherland)
• Narrow admissible Tuples (related to the Polymath project on prime gaps) (Andrew Sutherland)
• 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)

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Last modified 13th May 2021