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A014603 Discriminants of imaginary quadratic fields with class number 2 (negated). 29
15, 20, 24, 35, 40, 51, 52, 88, 91, 115, 123, 148, 187, 232, 235, 267, 403, 427 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..18.

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

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

(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

CROSSREFS

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

Cf. A191410.

Sequence in context: A133288 A322710 A316743 * A070222 A143321 A066860

Adjacent sequences:  A014600 A014601 A014602 * A014604 A014605 A014606

KEYWORD

nonn,fini,full,nice

AUTHOR

Eric Rains (rains(AT)caltech.edu)

EXTENSIONS

Offset corrected by Jianing Song, Aug 29 2018

STATUS

approved

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Last modified July 14 19:48 EDT 2020. Contains 335729 sequences. (Running on oeis4.)