A046020 -id:A046020 - 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]

A046016 Discriminants of imaginary quadratic fields with class number 19 (negated).

Original entry on oeis.org

311, 359, 919, 1063, 1543, 1831, 2099, 2339, 2459, 3343, 3463, 3467, 3607, 4019, 4139, 4327, 5059, 5147, 5527, 5659, 6803, 8419, 8923, 8971, 9619, 10891, 11299, 15091, 15331, 16363, 16747, 17011, 17299, 17539, 17683, 19507, 21187, 21211, 21283, 23203, 24763, 26227, 27043, 29803, 31123, 37507, 38707

Offset: 1

Eric W. Weisstein

47 discriminants in this sequence (proved).

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Reap[ For[ n = 1, n < 40000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 19, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

Original entry on oeis.org

95, 111, 164, 183, 248, 260, 264, 276, 295, 299, 308, 371, 376, 395, 420, 452, 456, 548, 552, 564, 579, 580, 583, 616, 632, 651, 660, 712, 820, 840, 852, 868, 904, 915, 939, 952, 979, 987, 995, 1032, 1043, 1060, 1092, 1128, 1131, 1155, 1195, 1204

Offset: 1

Eric W. Weisstein

131 discriminants in this sequence (almost certainly but not proved).

Andrew Howroyd, Table of n, a(n) for n = 1..131
Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A305416.

Cf. A191410.

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[6400], NumberFieldClassNumber[Sqrt[-#]] == 8 &]] (* Jean-François Alcover, Jun 27 2012 *)

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 8} \\ Andrew Howroyd, Jul 20 2018

[n for n in (1..6500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==8] # G. C. Greubel, Mar 01 2019

A046012 Discriminants of imaginary quadratic fields with class number 15 (negated).

Original entry on oeis.org

239, 439, 751, 971, 1259, 1327, 1427, 1567, 1619, 2243, 2647, 2699, 2843, 3331, 3571, 3803, 4099, 4219, 5003, 5227, 5323, 5563, 5827, 5987, 6067, 6091, 6211, 6571, 7219, 7459, 7547, 8467, 8707, 8779, 9043, 9907, 10243, 10267, 10459, 10651

Offset: 1

Eric W. Weisstein

68 discriminants in this sequence (proved).

R. J. Mathar, Table of n, a(n) for n=1..68 (full sequence)
Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Reap[ For[n = 1, n < 12000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 15, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A081319 Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

Original entry on oeis.org

1, 5, 23, 14, 47, 26, 71, 41, 199, 74, 167, 89, 191, 101, 239, 146, 383, 293, 311, 194, 431, 269, 647, 329, 479, 314, 983, 341, 887, 461, 719, 446, 839, 614, 1031, 626, 1487, 1199, 1439, 689, 1151, 794, 1847, 854, 1319, 941, 3023, 1106, 1511, 1109, 1559

Offset: 1

Dean Hickerson, Mar 18 2003

nonn

			From _Jianing Song_, May 08 2021: (Start)
a(6) = min{A060649(6), A344072(3)/4} = min{87, 104/4} = 26.
a(12) = min{A060649(12), A344072(6)/4} = min{231, 356/4} = 89.
a(18) = min{A060649(12), A344072(9)/4} = min{335, 1172/4} = 293.
a(38) = min{A060649(38), A344072(19)/4} = min{1199, 4916/4} = 1199. (End)

Robert G. Wilson v, Table of n, a(n) for n = 1..4500
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.

Cf. A060649, A038552, A046125, A014602-A046020.

t[] := 0; k = -1; While[k > -3100, a = NumberFieldClassNumber@Sqrt@k; If[t[a] == 0, t[a] = -k; Print[{a, -k}]]; k--]; t /@ Range@51 (* _Robert G. Wilson v, Sep 25 2017 *)

a(n) = A060649(n) for odd n > 1. For even n, assuming that A060649(n) > 0 and A344072(n/2) > 0, a(n) = min{A060649(n), A344072(n/2)/4}. - Jianing Song, May 08 2021

Edited by Max Alekseyev, Apr 28 2010

Escape clause added by Jianing Song, May 08 2021

A046008 Discriminants of imaginary quadratic fields with class number 11 (negated).

Original entry on oeis.org

167, 271, 659, 967, 1283, 1303, 1307, 1459, 1531, 1699, 2027, 2267, 2539, 2731, 2851, 2971, 3203, 3347, 3499, 3739, 3931, 4051, 5179, 5683, 6163, 6547, 7027, 7507, 7603, 7867, 8443, 9283, 9403, 9643, 9787, 10987, 13003, 13267, 14107, 14683, 15667

Offset: 1

Eric W. Weisstein

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Cf. A191410.

Reap[ For[n = 1, n < 15000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 11, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 11};
for(n=1, 16000, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019

[n for n in (1..16000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==11] # G. C. Greubel, Mar 01 2019

a(40)-a(41) from Giovanni Resta, Mar 20 2013

A046010 Discriminants of imaginary quadratic fields with class number 13 (negated).

Original entry on oeis.org

191, 263, 607, 631, 727, 1019, 1451, 1499, 1667, 1907, 2131, 2143, 2371, 2659, 2963, 3083, 3691, 4003, 4507, 4643, 5347, 5419, 5779, 6619, 7243, 7963, 9547, 9739, 11467, 11587, 11827, 11923, 12043, 14347, 15787, 16963, 20563

Offset: 1

Eric W. Weisstein

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Reap[ For[n = 1, n < 21000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 13, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A046014 Discriminants of imaginary quadratic fields with class number 17 (negated).

Original entry on oeis.org

383, 991, 1091, 1571, 1663, 1783, 2531, 3323, 3947, 4339, 4447, 4547, 4651, 5483, 6203, 6379, 6451, 6827, 6907, 7883, 8539, 8731, 9883, 11251, 11443, 12907, 13627, 14083, 14779, 14947, 16699, 17827, 18307, 19963, 21067, 23563, 24907, 25243, 26083, 26107, 27763, 31627, 33427, 36523, 37123

Offset: 1

Eric W. Weisstein

45 discriminants in this sequence (proved).

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Reap[ For[n = 1, n < 40000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 17, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A048925 Discriminants of imaginary quadratic fields with class number 24 (negated).

Original entry on oeis.org

695, 759, 1191, 1316, 1351, 1407, 1615, 1704, 1736, 1743, 1988, 2168, 2184, 2219, 2372, 2408, 2479, 2660, 2696, 2820, 2824, 2852, 2856, 2915, 2964, 3059, 3064, 3127, 3128, 3444, 3540, 3560, 3604, 3620, 3720, 3864, 3876, 3891, 3899, 3912

Offset: 0

Eric W. Weisstein

Andy Huchala, Table of n, a(n) for n = 0..510 (first 40 terms from Eric Weisstein)
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

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

Reap[ For[n = 1, n < 4000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 24, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

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] == 24] # Andy Huchala, Feb 15 2022

A046003 Discriminants of imaginary quadratic fields with class number 6 (negated).

Original entry on oeis.org

87, 104, 116, 152, 212, 244, 247, 339, 411, 424, 436, 451, 472, 515, 628, 707, 771, 808, 835, 843, 856, 1048, 1059, 1099, 1108, 1147, 1192, 1203, 1219, 1267, 1315, 1347, 1363, 1432, 1563, 1588, 1603, 1843, 1915, 1963, 2227, 2283, 2443, 2515, 2563, 2787, 2923, 3235, 3427, 3523, 3763

Offset: 1

Eric W. Weisstein

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Keith Matthews, Tables of imaginary quadratic fields with small class numbers.
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Cf. A191410.

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[3800], NumberFieldClassNumber[Sqrt[-#]] == 6 &]] (* Jean-François Alcover, Jun 27 2012 *)

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 6};
for(n=1, 4000, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019

[n for n in (1..4000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==6] # G. C. Greubel, Mar 01 2019

More terms from Seiichi Manyama, Jun 03 2018

cp's OEIS Frontend

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

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A046016 Discriminants of imaginary quadratic fields with class number 19 (negated).

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A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

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A046012 Discriminants of imaginary quadratic fields with class number 15 (negated).

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Mathematica

A081319 Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

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A046008 Discriminants of imaginary quadratic fields with class number 11 (negated).

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Sage

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A046010 Discriminants of imaginary quadratic fields with class number 13 (negated).

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Mathematica

A046014 Discriminants of imaginary quadratic fields with class number 17 (negated).

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Mathematica

A048925 Discriminants of imaginary quadratic fields with class number 24 (negated).

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