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A014602 Discriminants of imaginary quadratic fields with class number 1 (negated). 28
3, 4, 7, 8, 11, 19, 43, 67, 163 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Only fundamental discriminants are listed. The non-fundamental discriminants -12, -16, -27, and -28 also have class number 1 (and there are no others). [From Andrew V. Sutherland, Apr 19 2009]

REFERENCES

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

D. A. Cox, Primes of the form x^2+ny^2, Wiley, p. 271.

Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013; http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf

J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 483.

LINKS

Table of n, a(n) for n=1..9.

Eric Weisstein's World of Mathematics, Class Number

Index entries for sequences related to quadratic fields

MATHEMATICA

Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[200], NumberFieldClassNumber[ Sqrt[-#]] == 1 &]] (* Jean-Fran├žois Alcover, Jan 04 2012 *)

PROG

(PARI) is(n)=isfundamental(-n) && qfbclassno(-n)==1 \\ Charles R Greathouse IV, Nov 20 2012

CROSSREFS

Cf. A003173, A013658, A014603, A046002, ..., A046020.

Sequence in context: A192051 A033195 A050032 * A078823 A045615 A211220

Adjacent sequences:  A014599 A014600 A014601 * A014603 A014604 A014605

KEYWORD

nonn,fini,full,nice

AUTHOR

Eric Rains (rains(AT)caltech.edu)

STATUS

approved

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Last modified April 20 23:07 EDT 2014. Contains 240824 sequences.