OFFSET
1,1
COMMENTS
Includes only fundamental discriminants. The list of non-fundamental imaginary quadratic discriminants with class number 2 (negated) is 32, 36, 48, 60, 64, 72, 75, 99, 100, 112, 147. - Andrew V. Sutherland, Apr 08 2010 [These numbers are listed in A322710. - Jianing Song, Dec 07 2025]
REFERENCES
H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.
LINKS
Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland, and Angela Wong, A framework for deterministic primality proving using elliptic curves with complex multiplication, arXiv:1404.0107 [math.NT], 2014.
Alexandre Gélin, Everett W. Howe, and Christophe Ritzenthaler, Principally Polarized Squares of Elliptic Curves with Field of Moduli Equal To Q, arXiv:1806.03826 [math.NT], 2018 (see table 1 page 4).
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
Eric Weisstein's World of Mathematics, Class Number.
MATHEMATICA
Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[500], NumberFieldClassNumber[ Sqrt[-#]] == 2 &]] (* Jean-François Alcover, Jan 04 2012 *)
PROG
(PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 2} \\ Andrew Howroyd, Jul 20 2018
(SageMath) [n for n in (1..500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==2] # G. C. Greubel, Mar 01 2019
CROSSREFS
KEYWORD
nonn,fini,full,nice
AUTHOR
Eric Rains (rains(AT)caltech.edu)
EXTENSIONS
Offset corrected by Jianing Song, Aug 29 2018
STATUS
approved