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

1,1

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

Prog

(SageMath)
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]

Crossrefs

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

Sequence in context: A260067 A031903 A226851 * A158410 A108903 A167780

Adjacent sequences: A351671 A351672 A351673 * A351675 A351676 A351677

Keyword

nonn,fini,full

Author

Andy Huchala, Mar 27 2022

Status

approved