A014603 Discriminants of imaginary quadratic fields with class number 2 (negated).

15, 20, 24, 35, 40, 51, 52, 88, 91, 115, 123, 148, 187, 232, 235, 267, 403, 427

Offset: 1

Author

Eric Rains (rains(AT)caltech.edu)

Keywords

• nonn
• fini
• full
• nice

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

References

• H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.

Links

• A. Abatzoglou, A. Silverberg, A. V. Sutherland, A, 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.
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A006203, A013658, A014602, A046002, ..., A046020.

Cf. A191410.

Programs

Mathematica

Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[500], NumberFieldClassNumber[ Sqrt[-#]] == 2 &]] (* Jean-François Alcover, Jan 04 2012 *)

PARI

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 2} \\ Andrew Howroyd, Jul 20 2018

Sage

[n for n in (1..500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==2] # G. C. Greubel, Mar 01 2019

Extensions

Offset corrected by Jianing Song, Aug 29 2018