A013658 Discriminants of imaginary quadratic fields with class number 4 (negated).

39, 55, 56, 68, 84, 120, 132, 136, 155, 168, 184, 195, 203, 219, 228, 259, 280, 291, 292, 312, 323, 328, 340, 355, 372, 388, 408, 435, 483, 520, 532, 555, 568, 595, 627, 667, 708, 715, 723, 760, 763, 772, 795, 955, 1003, 1012, 1027, 1227, 1243, 1387, 1411, 1435, 1507, 1555

Offset: 1

Author

Eric Rains (rains(AT)caltech.edu)

Keywords

• nonn
• fini
• full

References

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..54 (full sequence, from Weisstein's World of Mathematics)
• 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
• Sung Sik Woo, Cubic formula and cubic curves, Commun. Korean Math. Soc. 28 (2013), No. 2, pp. 209-224.
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A014603, A046005, A192322.

Programs

Mathematica

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[1250], NumberFieldClassNumber[Sqrt[-#]] == 4 &]] (* Jean-François Alcover, Jun 27 2012 *)

PARI

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 4} \\ Andrew Howroyd, Jul 20 2018

Sage

[n for n in (1..2000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==4] # G. C. Greubel, Mar 01 2019

Extensions

a(50)-a(54) added by Andrew Howroyd, Jul 20 2018