A351674 Discriminants of imaginary quadratic fields with class number 36 (negated).

959, 1055, 1295, 1599, 1727, 1967, 2199, 2504, 2516, 2895, 3055, 3495, 3656, 3711, 3716, 3896, 3956, 4164, 4255, 4280, 4388, 4472, 4615, 4619, 4623, 4664, 4772, 5007, 5048, 5055, 5063, 5156, 5240, 5291, 5316, 5343, 5455, 5636, 5732, 5767, 5960, 6015, 6055

Offset: 1

Author

Andy Huchala, Mar 27 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 668 terms; largest is 217627.

The class groups associated to 255 of the above discriminants are isomorphic to C_36, 374 have a class group isomorphic to C_18 X C_2, 16 have a class group isomorphic to C_12 X C_3, and the remaining 23 have a class group isomorphic to C_6 X C_6.

Links

• Andy Huchala, Table of n, a(n) for n = 1..668
• Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
• Eric Weisstein's World of Mathematics, Class Number

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351680.

Programs

Sage

ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];
[-a[0] for a in ls if a[1] == 36]