A330219 Negative discriminants with form class group isomorphic to C_4 (negated).

39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 252, 256, 259, 275, 291, 292, 323, 328, 355, 363, 387, 388, 400, 475, 507, 568, 592, 603, 667, 723, 763, 772, 955, 1003, 1027, 1227, 1243, 1387, 1411, 1467, 1507, 1555

Offset: 1

Author

Jianing Song, Dec 05 2019

Keywords

• nonn
• fini

Comments

It seems that this is the full list.

Equivalently, negative discriminants of orders whose class group is isomorphic to C_4 (negated). - Jianing Song, May 17 2021

Links

• Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013

Crossrefs

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).

Subsequence of A133676 and A317987. Cf. also A013658.

Programs

PARI

isA330219(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[4] \\ Jianing Song, May 17 2021