A014603 -id:A014603 - cp's OEIS frontend

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

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

A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).

Original entry on oeis.org

119, 143, 159, 296, 303, 319, 344, 415, 488, 611, 635, 664, 699, 724, 779, 788, 803, 851, 872, 916, 923, 1115, 1268, 1384, 1492, 1576, 1643, 1684, 1688, 1707, 1779, 1819, 1835, 1891, 1923, 2152, 2164, 2363, 2452, 2643, 2776, 2836, 2899, 3028

Offset: 1

Eric W. Weisstein

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

Andrew Howroyd, Table of n, a(n) for n = 1..87
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.

Cf. A191410.

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[14000], NumberFieldClassNumber[Sqrt[-#]] == 10 &]] (* Jean-François Alcover, Jun 27 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 10} \\ Andrew Howroyd, Jul 24 2018

[n for n in (1..3500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==10] # G. C. Greubel, Mar 01 2019

A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).

Original entry on oeis.org

231, 255, 327, 356, 440, 516, 543, 655, 680, 687, 696, 728, 731, 744, 755, 804, 888, 932, 948, 964, 984, 996, 1011, 1067, 1096, 1144, 1208, 1235, 1236, 1255, 1272, 1336, 1355, 1371, 1419, 1464, 1480, 1491, 1515, 1547, 1572, 1668, 1720, 1732

Offset: 1

Eric W. Weisstein

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

Andrew Howroyd, Table of n, a(n) for n = 1..206
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.

Cf. A191410.

Reap[ For[n = 1, n < 2000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 12, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ Andrew Howroyd, Jul 24 2018

[n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==12] # G. C. Greubel, Mar 01 2019

A046011 Discriminants of imaginary quadratic fields with class number 14 (negated).

Original entry on oeis.org

215, 287, 391, 404, 447, 511, 535, 536, 596, 692, 703, 807, 899, 1112, 1211, 1396, 1403, 1527, 1816, 1851, 1883, 2008, 2123, 2147, 2171, 2335, 2427, 2507, 2536, 2571, 2612, 2779, 2931, 2932, 3112, 3227, 3352, 3579, 3707, 3715, 3867, 3988

Offset: 1

Eric W. Weisstein

There are 95 discriminants in this sequence (almost certainly but not proved).

Andrew Howroyd, Table of n, a(n) for n = 1..95
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.

Reap[ For[n = 1, n < 4000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 14, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 14} \\ Andrew Howroyd, Jul 24 2018

A046013 Discriminants of imaginary quadratic fields with class number 16 (negated).

Original entry on oeis.org

399, 407, 471, 559, 584, 644, 663, 740, 799, 884, 895, 903, 943, 1015, 1016, 1023, 1028, 1047, 1139, 1140, 1159, 1220, 1379, 1412, 1416, 1508, 1560, 1595, 1608, 1624, 1636, 1640, 1716, 1860, 1876, 1924, 1983, 2004, 2019, 2040, 2056, 2072

Offset: 1

Eric W. Weisstein

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

Andrew Howroyd, Table of n, a(n) for n = 1..322
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.
Victor Y. Wang, On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields, arXiv preprint arXiv:1508.06552, 2015
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 < 3000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 16, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 16} \\ Andrew Howroyd, Jul 24 2018

A046015 Discriminants of imaginary quadratic fields with class number 18 (negated).

Original entry on oeis.org

335, 519, 527, 679, 1135, 1172, 1207, 1383, 1448, 1687, 1691, 1927, 2047, 2051, 2167, 2228, 2291, 2315, 2344, 2644, 2747, 2859, 3035, 3107, 3543, 3544, 3651, 3688, 4072, 4299, 4307, 4568, 4819, 4883, 5224, 5315, 5464, 5492, 5539, 5899

Offset: 1

Eric W. Weisstein

The class group of Q[sqrt(-d)] is isomorphic to C_3 X C_6 for d = 9748, 12067, 16627, 17131, 19651, 22443, 23683, 34027, 34507. For all other known d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_18. - Jianing Song, Dec 01 2019

Jianing Song, Table of n, a(n) for n = 1..150
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.

Reap[ For[n = 1, n < 6000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 18, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A123563 Discriminants of imaginary quadratic fields with class number 20 (negated).

Original entry on oeis.org

455, 615, 776, 824, 836, 920, 1064, 1124, 1160, 1263, 1284, 1460, 1495, 1524, 1544, 1592, 1604, 1652, 1695, 1739, 1748, 1796, 1880, 1887, 1896, 1928, 1940, 1956, 2136, 2247, 2360, 2404, 2407, 2483, 2487, 2532, 2552

Offset: 1

Eric W. Weisstein, Nov 19 2006

A finite sequence with exactly 350 terms.

Eric Weisstein's World of Mathematics, Class Number.

Cf. A006203, A013658, A014602, A014603, A046002, ..., A046016, A046018, A046020.

Reap[ For[n = 1, n < 3000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 20, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A305416 Negated discriminants of imaginary quadratic number fields whose class group is isomorphic to the Klein 8-group, C_2 x C_2 x C_2.

Original entry on oeis.org

420, 660, 840, 1092, 1155, 1320, 1380, 1428, 1540, 1848, 1995, 3003, 3315

Offset: 1

Vincenzo Librandi, Jun 12 2018

Intersection of A046005 and A003644. Note that A003644 = A014602 union A014603 union A192322 union {a(n)} union {5460}. - Jianing Song, Jul 12 2018

Alexandre Gélin, Everett W. Howe, and Christophe Ritzenthaler, Principally Polarized Squares of Elliptic Curves with Field of Moduli Equal To Q, arXiv:1806.03826 [math.NT], 2018 (see table 1 page 4).

Cf. A003644, A014602, A014603, A192322.

Subsequence of A046005 and A003644.

A046005 = Import["https://oeis.org/A046005/b046005.txt", "Table"][[All, 2]];
A003644 = Import["https://oeis.org/A003644/b003644.txt", "Table"][[All, 2]];
A046005 ~Intersection~ A003644 (* Jean-François Alcover, Sep 25 2019 *)

ok(n)={isfundamental(-n) && [2, 2, 2] == quadclassunit(-n).cyc} \\ Andrew Howroyd, Jul 20 2018

A316743 Discriminants of imaginary fields whose class group has exponent 2, negated.

Original entry on oeis.org

15, 20, 24, 35, 40, 51, 52, 84, 88, 91, 115, 120, 123, 132, 148, 168, 187, 195, 228, 232, 235, 267, 280, 312, 340, 372, 403, 408, 420, 427, 435, 483, 520, 532, 555, 595, 627, 660, 708, 715, 760, 795, 840, 1012, 1092, 1155, 1320, 1380, 1428, 1435, 1540, 1848, 1995, 2280, 3003, 3315, 5460

Offset: 1

Jianing Song, Jul 20 2018

This sequence lists the negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r, r > 0.
These are the negated fundamental discriminants in A133288.
Also numbers in A003644 but not in A014602. Equals A014603 union A192322 union A305416 union {5460}.

Shin-ichi Katayama, Rational Points on the Parabola and the Arithmetic of Related Algebraic Tori, J. Math. Tokushima Univ. (2024) Vol. 58, 11-31. See p. 30.
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
P. J. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith. 22 (1973), 117-124.

Cf. Negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r: A014602 (r=0), A014603 (r=1), A192322 (r=2), A305416 (r=3).

Subsequence of A003644 and A133288.

ok(n)={isfundamental(-n) && quadclassunit(-n).no > 1 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018

cp's OEIS Frontend

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

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

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A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).

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A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).

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A046011 Discriminants of imaginary quadratic fields with class number 14 (negated).

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PARI

A046013 Discriminants of imaginary quadratic fields with class number 16 (negated).

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PARI

A046015 Discriminants of imaginary quadratic fields with class number 18 (negated).

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A123563 Discriminants of imaginary quadratic fields with class number 20 (negated).

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