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A014603
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Discriminants of imaginary quadratic fields with class number 2 (negated).
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45
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15, 20, 24, 35, 40, 51, 52, 88, 91, 115, 123, 148, 187, 232, 235, 267, 403, 427
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.
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LINKS
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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
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MATHEMATICA
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Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[500], NumberFieldClassNumber[ Sqrt[-#]] == 2 &]] (* Jean-François Alcover, Jan 04 2012 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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Eric Rains (rains(AT)caltech.edu)
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EXTENSIONS
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Offset corrected by Jianing Song, Aug 29 2018
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STATUS
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approved
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