A143748 Complete list of discriminants of definite Eichler orders with class number 2.

1, 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 41, 49, 81, 148, 169, 229, 257, 316, 321, 361, 404, 469, 568, 725, 1125, 1600, 1957, 2000, 2048, 2225, 2304, 2525, 2624, 2777, 3981, 4205, 4352, 4752, 6809, 14641, 24217, 36497, 38569, 300125, 371293, 434581, 485125, 592661

Offset

1,2

Comments

From Kirschmer and Voight, Table 8.3 in the arXiv version (Table 8.2 in the journal version): Definite Eichler orders with class number h = 2. A143747 is based on Table 8.2: Definite Eichler orders with class number h = 1.

Links

Table of n, a(n) for n=1..50.

Markus Kirschmer and John Voight, Algorithmic enumeration of ideal classes for quaternion orders, SIAM J. Comput., 39 (2010), 1714-1747; arXiv:0808.3833 [math.NT], 2008-2014. The published version has some errors that have been corrected in the arXiv version.

Example

With degree n = 6 there are 5 possible discriminants d_F = {300125, 371293, 434581, 485125, 592661} and in each case we must have norms D = N = 1.

Crossrefs

Cf. A143746, A143747.

Sequence in context: A396862 A003656 A003246 * A124378 A066299 A278040

Adjacent sequences: A143745 A143746 A143747 * A143749 A143750 A143751

Keyword

fini,full,nonn

Author

Jonathan Vos Post, Aug 30 2008

Extensions

Corrected by Andrei Zabolotskii, Oct 23 2025

Status

approved