A344408 - OEIS

A344408

Positive discriminants of orders of quadratic fields with class number 2.

40, 60, 65, 85, 96, 104, 105, 120, 136, 140, 156, 160, 165, 168, 185, 192, 200, 204, 205, 220, 221, 224, 232, 240, 252, 260, 264, 265, 273, 280, 285, 288, 296, 300, 305, 312, 320, 325, 336, 340, 345, 348, 352, 357, 360, 364, 365, 377, 380, 384, 385, 408

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Not to be confused with A391424, the positive discriminants of orders of quadratic fields with *form* class number 2. - Jianing Song, Dec 09 2025

Discriminants of orders of real quadratic fields whose form class group quotient by {I,-I} is isomorphic to C_2, where I is the principal class. (So I corresponds to the form x^2 - (D/4)*y^2 for 4|D and x^2 - x*y - ((D-1)/4)*y^2 for D == 1 (mod 4), and -I corresponds to the form (D/4)*x^2 - y^2 for 4|D and ((D-1)/4)*x^2 - x*y - y^2 for D == 1 (mod 4)). - Jianing Song, Dec 09 2025

The fundamental terms are listed in A094619.

LINKS

Jianing Song, Table of n, a(n) for n = 1..10001

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

PROG

(PARI) isA344408(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[2]

CROSSREFS

Cf. A322710 (the negative discriminant case), A094619.

Sequences related to the class numbers of real quadratic fields:

| Class numbers | Form class no. |

-------------+---------------+----------------+

Fundamental | 1: A003656 | 1: A003655 |