1,2

By the Odlyzko bounds, there are only finitely many such fields and they have been explicitly enumerated (by Voight) and no field satisfying the bound with n => 9, for a total of 279 fields. Kirschmer and Voight (pp. 26-27) also enumerate the ideal classes explicitly, Abstract: We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.

John Voight, Enumeration of totally real number fields of bounded root discriminant, Algorithmic number theory, eds. Alfred van der Poorten and Andreas Stein, Lecture notes in computer science, vol. 5011, Springer, Berlin, 2008, 268-281.

Markus Kirschmer and John Voight, Algorithmic enumeration of ideal classes for quaternion orders, Aug 28, 2008.

Sequence in context: A061756 A119028 A046512 this_sequence A064399 A050439 A053181

Adjacent sequences: A143743 A143744 A143745 this_sequence A143747 A143748 A143749

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 30 2008