A351664 -id:A351664 - cp's OEIS frontend

A351680 Discriminants of imaginary quadratic fields with class number 42 (negated).

1959, 2183, 2911, 3039, 3176, 3687, 3831, 4039, 4103, 4184, 4735, 4904, 4952, 5288, 5935, 5959, 6179, 6452, 6487, 6611, 6623, 6632, 6836, 7447, 7604, 7811, 7892, 7988, 8459, 8552, 8579, 8744, 8852, 9368, 9428, 9607, 10231, 10643, 10772, 10996, 11023, 11099

Offset: 1

Andy Huchala, Mar 28 2022

Sequence contains 339 terms; largest is 280267.

The class group of Q[sqrt(-d)] is isomorphic to C_42 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..339
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-A351679.

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] == 42]

A351666 Discriminants of imaginary quadratic fields with class number 28 (negated).

Original entry on oeis.org

831, 935, 1095, 1311, 1335, 1364, 1455, 1479, 1496, 1623, 1703, 1711, 1855, 1976, 2024, 2055, 2120, 2127, 2324, 2359, 2431, 2455, 2564, 2607, 2616, 2703, 3224, 3272, 3396, 3419, 3487, 3535, 3572, 3576, 3608, 3624, 3731, 3848, 3995, 4040, 4183, 4279, 4344

Offset: 1

Andy Huchala, Feb 16 2022

Sequence contains 457 terms; largest is 126043.

The class groups associated to 174 of the above discriminants are isomorphic to C_28, and the remaining 283 have a class group isomorphic to C_14 X C_2.

Andy Huchala, Table of n, a(n) for n = 1..457
Eric Weisstein's World of Mathematics, Class Number

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

isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 28}; \\ Michel Marcus, Mar 02 2022

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] == 28]

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

Original entry on oeis.org

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]

A351665 Discriminants of imaginary quadratic fields with class number 27 (negated).

Original entry on oeis.org

983, 1231, 1399, 1607, 1759, 1879, 1999, 3271, 3299, 3943, 4903, 6007, 6011, 7699, 8867, 10531, 10939, 11003, 11027, 11383, 11491, 11779, 11939, 13411, 14243, 14723, 15107, 15739, 16411, 16547, 17443, 17627, 17659, 17747, 18587, 18787, 18859, 19051, 19427

Offset: 1

Andy Huchala, Feb 16 2022

Sequence contains 93 terms; largest is 103387.

The class group of Q[sqrt(-d)] is isomorphic to C_9 X C_3 for d = 3299, 19427, 34603, 89923, and 98443. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_27.

Andy Huchala, Table of n, a(n) for n = 1..93
Eric Weisstein's World of Mathematics, Class Number

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

isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 27}; \\ Michel Marcus, Mar 02 2022

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] == 27]

A351667 Discriminants of imaginary quadratic fields with class number 29 (negated).

Original entry on oeis.org

887, 2287, 2311, 2383, 2939, 3583, 3659, 3823, 4451, 4519, 5051, 5743, 6947, 7207, 7643, 7687, 8863, 8963, 9323, 12323, 13763, 13883, 14387, 15139, 15227, 15443, 15467, 15859, 16427, 17491, 20483, 20507, 22051, 23059, 23251, 24859, 25523, 28403, 29587, 29723

Offset: 1

Andy Huchala, Mar 24 2022

Sequence contains 83 terms; largest is 166147.

The class group of Q[sqrt(-d)] is isomorphic to C_29 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..83
Eric Weisstein's World of Mathematics, Class Number

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351666.

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] == 29]

A351668 Discriminants of imaginary quadratic fields with class number 30 (negated).

Original entry on oeis.org

671, 815, 1007, 1844, 2036, 2071, 2191, 2264, 2319, 2599, 2708, 3188, 3223, 3284, 3439, 3991, 4087, 4276, 4696, 4835, 4859, 4979, 5579, 5912, 6107, 6459, 6463, 6488, 6535, 6635, 7087, 7115, 7303, 7576, 7835, 7971, 8259, 8267, 8367, 8483, 8948, 9019, 9076

Offset: 1

Andy Huchala, Mar 24 2022

Sequence contains 255 terms; largest is 134467.

The class group of Q[sqrt(-d)] is isomorphic to C_30 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..255
Eric Weisstein's World of Mathematics, Class Number

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

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] == 30]

A351669 Discriminants of imaginary quadratic fields with class number 31 (negated).

Original entry on oeis.org

719, 911, 2927, 3251, 3727, 3779, 4159, 4951, 5651, 6131, 6491, 7639, 8647, 9203, 10427, 11863, 12347, 12923, 13043, 13219, 13687, 14627, 14731, 15923, 17987, 18803, 19219, 20611, 24691, 24979, 28051, 32083, 32363, 35491, 38851, 39667, 39883, 41227, 41539

Offset: 1

Andy Huchala, Mar 24 2022

Sequence contains 73 terms; largest is 133387.

The class group of Q[sqrt(-d)] is isomorphic to C_31 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..73
Eric Weisstein's World of Mathematics, Class Number

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

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] == 31]

A351670 Discriminants of imaginary quadratic fields with class number 32 (negated).

Original entry on oeis.org

791, 1119, 1239, 1463, 1551, 1767, 1784, 1943, 2084, 2180, 2276, 2343, 2840, 2847, 2996, 3080, 3156, 3199, 3207, 3236, 3247, 3295, 3428, 3476, 3679, 3812, 3895, 4088, 4296, 4340, 4495, 4584, 4647, 4767, 4868, 4884, 4964, 4980, 4996, 5012, 5064, 5192, 5215

Offset: 1

Andy Huchala, Mar 24 2022

Sequence contains 708 terms; largest is 164803.

The class groups associated to 187 of the above discriminants are isomorphic to C_32, 273 have a class group isomorphic to C_16 X C_2, 160 isomorphic to C_8 X C_2 X C_2, 60 have a class group isomorphic to C_8 X C_4, 15 have a class group isomorphic to C_4 X C_2 X C_2 X C_2, and the remaining 13 have a class group isomorphic to C_4 X C_4 X C_2.

Andy Huchala, Table of n, a(n) for n = 1..708
Eric Weisstein's World of Mathematics, Class Number

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

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] == 32]

A351671 Discriminants of imaginary quadratic fields with class number 33 (negated).

Original entry on oeis.org

839, 1583, 1951, 2423, 3967, 4091, 4423, 4567, 4663, 4831, 4999, 5167, 5623, 5791, 6343, 6823, 6967, 7331, 7351, 7499, 8167, 9011, 12619, 13183, 13619, 13931, 14251, 15299, 16619, 17419, 18691, 19163, 21347, 21563, 24019, 25411, 28027, 28163, 28579, 29243

Offset: 1

Andy Huchala, Mar 25 2022

Sequence contains 101 terms; largest is 222643.

The class group of Q[sqrt(-d)] is isomorphic to C_33 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..101
Eric Weisstein's World of Mathematics, Class Number

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

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] == 33]

A351673 Discriminants of imaginary quadratic fields with class number 35 (negated).

Original entry on oeis.org

1031, 1223, 2087, 2239, 2543, 4259, 4931, 5171, 5939, 6899, 7211, 7451, 7523, 8219, 8363, 8699, 9007, 9419, 10979, 11411, 11503, 12007, 14939, 15803, 16451, 16651, 17123, 18451, 19259, 20731, 22787, 23011, 24203, 24547, 26387, 26723, 28411, 33619, 36643

Offset: 1

Andy Huchala, Mar 25 2022

Sequence contains 103 terms; largest is 210907.

The class group of Q[sqrt(-d)] is isomorphic to C_35 for all d in this sequence.

Andy Huchala, Table of n, a(n) for n = 1..103
Eric Weisstein's World of Mathematics, Class Number

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

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] == 35]

cp's OEIS Frontend

A351680 Discriminants of imaginary quadratic fields with class number 42 (negated).

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A351666 Discriminants of imaginary quadratic fields with class number 28 (negated).

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

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A351665 Discriminants of imaginary quadratic fields with class number 27 (negated).

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A351667 Discriminants of imaginary quadratic fields with class number 29 (negated).

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A351668 Discriminants of imaginary quadratic fields with class number 30 (negated).

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A351669 Discriminants of imaginary quadratic fields with class number 31 (negated).

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A351670 Discriminants of imaginary quadratic fields with class number 32 (negated).

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Sage

A351671 Discriminants of imaginary quadratic fields with class number 33 (negated).

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