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A351678
Discriminants of imaginary quadratic fields with class number 40 (negated).
1
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
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]
KEYWORD
nonn,fini,full
AUTHOR
Andy Huchala, Mar 27 2022
STATUS
approved