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Discriminants of imaginary quadratic fields with class number 2 (negated).
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%I #37 Mar 01 2019 16:28:27

%S 15,20,24,35,40,51,52,88,91,115,123,148,187,232,235,267,403,427

%N Discriminants of imaginary quadratic fields with class number 2 (negated).

%C 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

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

%H A. Abatzoglou, A. Silverberg, A. V. Sutherland, A, Wong, <a href="http://arxiv.org/abs/1404.0107">A framework for deterministic primality proving using elliptic curves with complex multiplication</a>, arXiv:1404.0107 [math.NT], 2014.

%H Alexandre Gélin, Everett W. Howe, and Christophe Ritzenthaler, <a href="https://arxiv.org/abs/1806.03826">Principally Polarized Squares of Elliptic Curves with Field of Moduli Equal To Q</a>, arXiv:1806.03826 [math.NT], 2018 (see table 1 page 4).

%H Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Union[ (-NumberFieldDiscriminant[ Sqrt[-#]] &) /@ Select[ Range[500], NumberFieldClassNumber[ Sqrt[-#]] == 2 &]] (* _Jean-François Alcover_, Jan 04 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 2} \\ _Andrew Howroyd_, Jul 20 2018

%o (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

%Y Cf. A006203, A013658, A014602, A046002, ..., A046020.

%Y Cf. A191410.

%K nonn,fini,full,nice

%O 1,1

%A Eric Rains (rains(AT)caltech.edu)

%E Offset corrected by _Jianing Song_, Aug 29 2018