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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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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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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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STATUS
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approved
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