Lehrstuhl D für Mathematik
Database of unit groups
Database: Unit Groups of Orders

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