A351678 Discriminants of imaginary quadratic fields with class number 40 (negated).

1271, 1839, 2255, 2415, 2559, 2751, 2756, 2919, 2936, 2959, 3044, 3135, 3255, 3399, 3423, 3524, 3704, 3927, 4004, 4047, 4071, 4407, 4607, 4760, 4807, 4820, 4836, 4856, 5060, 5143, 5191, 5304, 5367, 5727, 6020, 6036, 6212, 6324, 6807, 6980, 6996, 7063, 7080

Offset: 1

Author

Andy Huchala, Mar 27 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 912 terms; largest is 260947.

The class groups associated to 251 of the above discriminants are isomorphic to C_40, 438 have a class group isomorphic to C_20 X C_2, and the remaining 223 have a class group isomorphic to C_10 X C_2 X C_2.

Links

• Andy Huchala, Table of n, a(n) for n = 1..912
• 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] == 40]