Databases

A database of basic algebras for the p-modular group algebras of some of the smaller groups catalogued in the Atlas of Finite Groups.

Every group G where S ≤ G ≤ Aut(S) and S is a simple group of order less than 16,000,000, or S is one of M24, HS, J3, McL, Sz(32), or L6(2).

The number field database, comprising over 2.6 million number fields of degrees between 2 and 9 (inclusive).

The ATLAS database of finite group representations (283 groups).

Data used by the best known linear codes and best known quantum codes databases.

The classification of all 674,688 canonical Fano polytopes in dimension three. See the included README.txt for installation instructions.

Data for creating groups of order 3⁸.

Data needed by the elliptic curve primality proving routines.

John Cremona's database of all elliptic curves of conductor up to 499,999.

Data used internally by the integer factorisation routines.

A database of Fano 3-folds.

Data used internally by the finite field creation routines.

Tables for computing discrete logarithms in finite fields of characteristic 2 (complete up to GF(2⁴⁴⁰)).

Tables for computing discrete logarithms in finite fields of characteristic 3 (complete up to GF(3²⁶¹)).

Tables for computing discrete logarithms in finite fields of characteristic 5 (complete up to GF(5²⁰³)).

Tables for computing discrete logarithms in finite fields of characteristic 7 (complete up to GF(7¹⁵⁰)).

Tables for discrete logarithms in finite fields of characteristic p, where p is a small prime greater than 7 (covers p up to 97 for many fields).

Databases of function fields with specified base finite field and degree. Supported: F2 (d2,d3), F3 (d2), F4 (d2,d3,d5), F5 (d2,d3,d4,d8), F7 (d9), F11 (d3), F13 (d3).

Data used in the computation of Galois groups of number fields.

Data needed by the routines for working with analytic Jacobians of hyperelliptic curves.

Some strongly regular graphs with 25 to 40 vertices.

A database of automatic groups created from hyperbolic manifolds (currently 5,389 such automatic groups).

Known inequivalent Hadamard matrices of degree up to 256.

Known inequivalent skew-symmetric Hadamard matrices of degrees 36, 44, and 52.

Data used by the irreducible soluble subgroups database.

All K3 surfaces of genus −1, 0, 1, or 2, and others of genus up to 9.

A database of interesting lattices.

The classification of all LDP-polygons with index at most 17. See included README.txt for installation instructions.

The classification of all l-reflexive polygons up to index 200. See included README.txt for installation instructions.

The fundamental groups of the 10,986 small-volume closed hyperbolic manifolds in the Hodgson–Weeks census.

Databases of classical, canonical, and Atkin modular polynomials.

The extended database of Atkin modular polynomials for primes between 400 and 1000. Note: 13 primes between 800 and 1000 are not in this database.

All perfect groups up to order 50,000, and many classes up to order one million, defined by finite presentations with permutation representations.

All primitive permutation groups of degree less than 2500.

A database of quaternionic matrix groups.

A database of rational maximal finite matrix groups and their invariant forms, for small dimensions (up to 31).

A database of irreducible QG-modules, where G is a finite group and Q is the rational field (most irreducible rational representations of ATLAS groups up to degree 1000).

A database of symplectic matrix groups.

All groups of order up to 2000 (excl. order 1024); all groups whose order is the product of at most 3 primes; all groups of order dividing p⁶; all groups of order pqⁿ where qⁿ divides 2⁸, 3⁶, 5⁵, or 7⁴.

The classification of all polygons, up to translation and change of basis, that fit inside a [0,7] × [0,7] box. See included README.txt for installation instructions.

All nonsingular Fano polytopes up to dimension 6: 5 classes (dim 2), 18 (dim 3), 124 (dim 4), 866 (dim 5), 7,622 (dim 6). See included README.txt for installation instructions.

The classification of all 72,256 nonsingular Fano polytopes in dimension 7. See included README.txt for installation instructions.

The classification of all 749,892 nonsingular Fano polytopes in dimension 8. See included README.txt for installation instructions.

The classification of the semisimple subalgebras of the simple Lie algebras of rank up to 8.

The classification of all 634 terminal Fano polytopes in dimension three. See included README.txt for installation instructions.

A database of groups with trivial Fitting subgroup, needed for the computation of conjugacy classes of subgroups.

Transitive group identification data for degree 32 (1.4 GB uncompressed).

All transitive permutation groups up to degree 31.

All transitive permutation groups of degree 32.