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Negative discriminants with form class number 2 (negated).
5

%I #17 May 17 2021 08:50:14

%S 15,20,24,32,35,36,40,48,51,52,60,64,72,75,88,91,99,100,112,115,123,

%T 147,148,187,232,235,267,403,427

%N Negative discriminants with form class number 2 (negated).

%C This is the full sequence.

%C The j-invariants for these discriminants are quadratic integers. See the links below for a full list.

%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 Jianing Song, <a href="/A322710/a322710.txt">j-invariants for the discriminants with form class number 2 and their Hilbert class polynomials</a>

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

%o (PARI) for(n=1, 500, if((-n)%4<=1&&quadclassunit(-n)[1]==2, print1(n, ", ")))

%Y Cf. A014603, A305474.

%Y Cf. A133675 (negative discriminants with form class group isomorphic to the trivial group), this sequence (isomorphic to C_2), A328825 (isomorphic to C_3), A329182 (isomorphic to C_2 X C_2), A330219 (isomorphic to C_4).

%K nonn,fini,full

%O 1,1

%A _Jianing Song_, Dec 24 2018