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 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).
The column "Z-discriminant" contains the absolute value of the Z-discriminant of the maximal order, i.e. the norm of the discriminant ideal of the maximal order multiplied with the absolute value of the discriminant of the number field.
The number fields are ordered by their discriminants.
Minimal Polynomial of alpha | a | b | Z-discriminant | Files |
x^2+3 | -7 | -2 | 147 | Link |
x^2+3 | -13 | -2 | 507 | Link |
x^2+1 | -5 | -2 | 100 | Link |
x^2+7 | -1 | -1 | 28 | Link |
x^2+7 | -1 | -11 | 847 | Link |
x^2+7 | -14 | -11 | 3388 | Link |
x^2+7 | -1 | -23 | 3703 | Link |
x^2+15 | -1 | -1 | 60 | Link |
x^2+15 | -17 | -31 | 4335 | Link |
x^2+15 | -1 | -19 | 5415 | Link |
x^2+5 | -7 | -2 | 980 | Link |
x^2+31 | -1 | -1 | 124 | Link |
x^2+55 | -1 | -1 | 220 | Link |
x^2+79 | -1 | -1 | 316 | Link |
x^2+95 | -1 | -1 | 380 | Link |
x^2+103 | -1 | -1 | 412 | Link |
x^2+111 | -1 | -1 | 444 | Link |
x^2+255 | -1 | -1 | 1020 | Link |