A329182 Negative discriminants with form class group isomorphic to C_2 X C_2 (negated).

84, 96, 120, 132, 160, 168, 180, 192, 195, 228, 240, 280, 288, 312, 315, 340, 352, 372, 408, 435, 448, 483, 520, 532, 555, 595, 627, 708, 715, 760, 795, 928, 1012, 1435

Offset: 1

Author

Jianing Song, Dec 05 2019

Keywords

• nonn
• fini
• full

Comments

This sequence is finite and this is the full list.

Equivalently, negative discriminants of orders whose class group is isomorphic to C_2 X C_2 (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), this sequence (isomorphic to C_2 X C_2), A330219 (isomorphic to C_4).

The fundamental terms are listed in A192322. Cf. also A013658.

Programs

PARI

isA329182(d) = (d>0) && ((d%4==0)||(d%4==3)) && quadclassunit(-d)[2]==[2,2] \\ Jianing Song, May 17 2021