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

1,1

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

Prog

(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]

Crossrefs

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

Sequence in context: A238286 A152507 A203100 * A378455 A377417 A273000

Adjacent sequences: A351675 A351676 A351677 * A351679 A351680 A351681

Keyword

nonn,fini,full

Author

Andy Huchala, Mar 27 2022

Status

approved