A351680 -id:A351680 - cp's OEIS frontend

A351679 Discriminants of imaginary quadratic fields with class number 41 (negated).

1151, 2551, 2719, 3079, 3319, 3511, 6143, 9319, 9467, 10499, 10903, 11047, 11483, 11719, 11987, 12227, 12611, 13567, 14051, 14411, 14887, 14983, 16067, 16187, 19763, 20407, 20771, 21487, 22651, 24971, 25171, 26891, 26987, 27739, 28547, 29059, 29251, 30859

Offset: 1

Andy Huchala, Mar 28 2022

Sequence contains 109 terms; largest is 296587.

The class group of Q[sqrt(-d)] is isomorphic to C_41 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..109
Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
Eric Weisstein's World of Mathematics, Class Number

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

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] == 41]

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

Original entry on oeis.org

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

Andy Huchala, Mar 27 2022

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.

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

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

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]

A351675 Discriminants of imaginary quadratic fields with class number 37 (negated).

Original entry on oeis.org

1487, 2447, 3391, 5839, 6367, 8147, 9803, 10739, 12343, 12583, 12967, 14767, 15259, 16927, 18947, 19403, 20011, 20147, 21139, 21587, 22807, 23371, 23627, 26731, 28283, 28307, 31699, 31723, 36691, 37171, 37243, 38371, 39139, 39451, 40531, 41659, 42283, 42443

Offset: 1

Andy Huchala, Mar 27 2022

Sequence contains 85 terms; largest is 158923.

The class group of Q[sqrt(-d)] is isomorphic to C_37 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..85
Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
Eric Weisstein's World of Mathematics, Class Number

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

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] == 37]

A351676 Discriminants of imaginary quadratic fields with class number 38 (negated).

Original entry on oeis.org

1199, 1535, 1671, 2031, 3047, 3415, 4916, 5127, 5528, 6423, 6548, 6559, 6927, 7016, 7091, 7135, 7444, 8276, 8315, 8651, 8939, 8983, 9179, 9487, 9524, 9659, 9727, 9908, 10216, 10715, 10779, 10984, 11432, 11463, 11507, 11915, 12779, 12904, 13667, 14099, 14164

Offset: 1

Andy Huchala, Mar 27 2022

Sequence contains 237 terms; largest is 289963.

The class group of Q[sqrt(-d)] is isomorphic to C_38 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..237
Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
Eric Weisstein's World of Mathematics, Class Number

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

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] == 38]

A351677 Discriminants of imaginary quadratic fields with class number 39 (negated).

Original entry on oeis.org

1439, 2207, 2791, 3767, 3919, 4111, 5099, 5119, 6199, 6779, 9059, 9967, 10091, 10163, 10399, 10567, 10667, 11743, 12539, 13163, 13523, 14843, 14867, 15607, 16087, 16139, 16787, 17383, 18127, 21851, 23027, 24499, 26539, 27827, 30211, 30347, 30803, 32027, 32491

Offset: 1

Andy Huchala, Mar 27 2022

Sequence contains 115 terms; largest is 253507.

The class group of Q[sqrt(-d)] is isomorphic to C_39 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..115
Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
Eric Weisstein's World of Mathematics, Class Number

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

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] == 39]

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

Original entry on oeis.org

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

Andy Huchala, Mar 27 2022

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.

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

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

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]

cp's OEIS Frontend

A351679 Discriminants of imaginary quadratic fields with class number 41 (negated).

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

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A351675 Discriminants of imaginary quadratic fields with class number 37 (negated).

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A351676 Discriminants of imaginary quadratic fields with class number 38 (negated).

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Sage

A351677 Discriminants of imaginary quadratic fields with class number 39 (negated).

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Sage

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

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Author

Keywords

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Crossrefs

Programs

Sage