Indefinite quaternion algebras over the rationals
In this table you can find MAGMA-readable files (simply download and use the "load"-command) containing our results for the S-unit group of a maximal order in the quaternion algebra defined by i^2=a, j^2=b, realized in the 2-by-2 matrix ring over the real quadratic field Q(alpha), where alpha is always a square root of b.
The file contains elements I and J corresponding to i and j respectively, a basis BB of the maximal order, a finitely presented group G, a list Gens corresponding to the generators of the S-unit group and finally a list CenterGens of elements of G corresponding to the generators of the center of the S-unit group.
The algebras are ordered by their discriminants.
a | b | Ramified primes | S | Files |
2 | 3 | 2, 3 | {5} | Link |
{7} | Link | |||
{11} | Link | |||
{5, 7} | Link | |||
{5, 11} | Link | |||
{7, 11} | Link | |||
{5, 7, 11} | Link | |||
-2 | 35 | 5, 7 | {2} | Link |
{3} | Link | |||
{11} | Link | |||
{2, 3} | Link | |||
{2 11} | Link | |||
{3, 11} | Link | |||
{2, 3, 11} | Link |