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A014603 Discriminants of imaginary quadratic fields with class number 2 (negated). 45
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
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.
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. A191410.
Sequence in context: A133288 A322710 A316743 * A070222 A143321 A066860
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 March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)