|
|
A014602
|
|
Discriminants of imaginary quadratic fields with class number 1 (negated).
|
|
52
|
|
|
|
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). - 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.
J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 483.
|
|
LINKS
|
|
|
MATHEMATICA
|
Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[200], NumberFieldClassNumber[ Sqrt[-#]] == 1 &]] (* Jean-François Alcover, Jan 04 2012 *)
|
|
PROG
|
(Sage)
is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 1
A014602 = lambda n: filter(is_fund_and_qfbcn_1, (-1, -2, ..-n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,fini,full,nice
|
|
AUTHOR
|
Eric Rains (rains(AT)caltech.edu)
|
|
STATUS
|
approved
|
|
|
|