

A014602


Discriminants of imaginary quadratic fields with class number 1 (negated).


28




OFFSET

1,1


COMMENTS

Only fundamental discriminants are listed. The nonfundamental 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 &]] (* JeanFrançois 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



