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A013658
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Discriminants of imaginary quadratic fields with class number 4 (negated).
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45
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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
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OFFSET
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1,1
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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[1250], NumberFieldClassNumber[Sqrt[-#]] == 4 &]] (* Jean-François Alcover, Jun 27 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,fini,full
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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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