login
Negative discriminants with form class group isomorphic to C_4 (negated).
3

%I #17 May 17 2021 08:50:31

%S 39,55,56,63,68,80,128,136,144,155,156,171,184,196,203,208,219,220,

%T 252,256,259,275,291,292,323,328,355,363,387,388,400,475,507,568,592,

%U 603,667,723,763,772,955,1003,1027,1227,1243,1387,1411,1467,1507,1555

%N Negative discriminants with form class group isomorphic to C_4 (negated).

%C It seems that this is the full list.

%C Equivalently, negative discriminants of orders whose class group is isomorphic to C_4 (negated). - _Jianing Song_, May 17 2021

%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

%o (PARI) isA330219(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[4] \\ _Jianing Song_, May 17 2021

%Y Cf. A133675 (negative discriminants with form class group isomorphic to the trivial group), A322710 (isomorphic to C_2), A328825 (isomorphic to C_3), A329182 (isomorphic to C_2 X C_2), this sequence (isomorphic to C_4).

%Y Subsequence of A133676 and A317987. Cf. also A013658.

%K nonn,fini

%O 1,1

%A _Jianing Song_, Dec 05 2019