A013658 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A014603, A046005, A192322.

Sequence in context: A133676 A317987 A330219 * A227735 A319983 A165346

Adjacent sequences: A013655 A013656 A013657 * A013659 A013660 A013661

KEYWORD

nonn,fini,full

AUTHOR

Eric Rains (rains(AT)caltech.edu)

EXTENSIONS

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

STATUS

approved