Quaternion algebras over imaginary quadratic number fields
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 over the imaginary quadratic field Q(alpha). We only list the norms of the prime ideals in S in the table.
The number fields are ordered by their discriminants.
Minimal Polynomial of alpha | a | b | S | Files |
x^2+3 | -2 | -7 | {3} | Link |
{4} | Link | |||
{13} | Link | |||
{19} | Link | |||
{3, 4} | Link | |||
{3, 13} | Link | |||
{3, 19} | Link | |||
{4, 13} | Link | |||
{4, 19} | Link | |||
{13, 19} | Link | |||
{3, 4, 13} | Link | |||
{3, 4, 19} | Link | |||
{3, 13, 19} | Link | |||
{4, 13, 19} | Link | |||
{3, 4, 13, 19} | Link | |||
x^2+1 | -2 | -5 | {2} | Link |
{9} | Link | |||
{13} | Link | |||
{17} | Link | |||
{2, 9} | Link | |||
{2, 13} | Link | |||
{2, 17} | Link | |||
{9, 13} | Link | |||
{9, 17} | Link | |||
{13, 17} | Link | |||
{2, 9, 13} | Link | |||
{2, 9, 17} | Link | |||
{2, 13, 17} | Link | |||
{9, 13, 17} | Link | |||
{2, 9, 13, 17} | Link | |||
x^2+7 | -1 | -1 | {7} | Link |
{9} | Link | |||
{11} | Link | |||
{7, 9} | Link | |||
{7, 11} | Link | |||
{9, 11} | Link | |||
{7, 9, 11} | Link |