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Rational Points on Ellptic Curves: y^2=x^3+n (n \in [1001..2000])


[2021.08.13]y^2=x^3+n (n \in [1001..2000])の有理点



■n=1001,1002,...,2000に対して、
     En: y2 = x3+n
の有理点を求める。

■n=1001,1002,...,2000に対して、楕円曲線Enのねじれ点群En(Q)torsを計算すると、
     En(Q)tors=Z/2Z if n=1728
                 =Z/3Z if n=1024,1089,1156,1225,1296,1269,1444,1521,1600,1681,1764,1849,1936
                 ={O} if nが平方数,立方数でない
となる。

[pari/gpによる計算]
gp> ec(n)=ellinit([0,0,0,0,n]);
gp> tg(n1,n2)=local(e,g,o);for(i=n1,n2,e=ec(i);g=elltors(e);o=g[1];if(o>1,print("E_",i,"(Q)_{tors}=",g)));
gp> tg(1001,2000)
E_1024(Q)_{tors}=[3, [3], [[0, 32]]]
E_1089(Q)_{tors}=[3, [3], [[0, 33]]]
E_1156(Q)_{tors}=[3, [3], [[0, 34]]]
E_1225(Q)_{tors}=[3, [3], [[0, 35]]]
E_1296(Q)_{tors}=[3, [3], [[0, 36]]]
E_1331(Q)_{tors}=[2, [2], [[-11, 0]]]
E_1369(Q)_{tors}=[3, [3], [[0, 37]]]
E_1444(Q)_{tors}=[3, [3], [[0, 38]]]
E_1521(Q)_{tors}=[3, [3], [[0, 39]]]
E_1600(Q)_{tors}=[3, [3], [[0, 40]]]
E_1681(Q)_{tors}=[3, [3], [[0, 41]]]
E_1728(Q)_{tors}=[2, [2], [[-12, 0]]]
E_1764(Q)_{tors}=[3, [3], [[0, 42]]]
E_1849(Q)_{tors}=[3, [3], [[0, 43]]]
E_1936(Q)_{tors}=[3, [3], [[0, 44]]]
time = 7 ms.

■楕円曲線EnのMordell-Weil群のrankと生成元を求めると以下のようになる。

- E~n: Y2Z=X3+nZ3
En: y2=x3+n
-
n [a1,a2,a3,a4,a6]
j(En)
Conductor of En
En(Q)tors
En(Q)torsの生成元
rank(En(Q)) En(Q)/En(Q)tors
の生成元 [X:Y:Z]
En(Q)/En(Q)tors
の生成元の高さ
En(Z)
Enの整点[x,y]
(where y >= 0)
n
1001 [0, 0, 0, 0, 1001]
0
108216108
{O}
-
2 [-10 : 1 : 1],
[92 : 883 : 1]
2.39008353807581,
4.12672176392503
[-10, 1], [92, 883], [22520, 3379501] 1001
1002 [0, 0, 0, 0, 1002]
0
433729728
{O}
-
1 [15564 : 71929 : 1728] 7.89216561928112
- 1002
1003 [0, 0, 0, 0, 1003]
0
434595888
{O}
-
1 [-26352 : 111175 : 4096] 8.35471015898845
- 1003
1004 [0, 0, 0, 0, 1004]
0
27216432
{O}
-
2 [-10 : 2 : 1],
[34 : 263 : 8]
2.15990410573715,
4.18570383203716
[-10, 2], [5645, 424127] 1004
1005 [0, 0, 0, 0, 1005]
0
109082700
{O}
-
1 [850596579 : -9549966194 : 6751269] 15.3686609411873
- 1005
1006 [0, 0, 0, 0, 1006]
0
437199552
{O}
-
2 [-30 : 247 : 8],
[10596 : 136355 : 64]
4.17034624534349,
7.91918730401791
- 1006
1007 [0, 0, 0, 0, 1007]
0
146023056
{O}
-
1 [7444385 : 39726708 : 274625] 11.3317006676821
- 1007
1008 [0, 0, 0, 0, 1008]
0
190512
{O}
-
0 - - - 1008
1009 [0, 0, 0, 0, 1009]
0
36650916
{O}
-
2 [-10 : 3 : 1],
[6 : 35 : 1]
1.84309098083929,
2.37456212589905
[-10, 3], [6, 35], [8, 39], [1355, 49878], [2520, 126503] 1009
1010 [0, 0, 0, 0, 1010]
0
440683200
{O}
-
1 [-6462 : 185219 : 5832] 8.55050704343178
- 1010
1011 [0, 0, 0, 0, 1011]
0
441556272
{O}
-
1 [826159 : -3671944 : 79507] 10.4943034650370
- 1011
1012 [0, 0, 0, 0, 1012]
0
6912972
{O}
-
0 - - - 1012
1013 [0, 0, 0, 0, 1013]
0
110826252
{O}
-
1 [5862415 : 28461386 : 274625] 11.7083026104136
- 1013
1014 [0, 0, 0, 0, 1014]
0
2628288
{O}
-
0 - - - 1014
1015 [0, 0, 0, 0, 1015]
0
445057200
{O}
-
0 - - - 1015
1016 [0, 0, 0, 0, 1016]
0
9290304
{O}
-
3 [2 : 32 : 1],
[22 : 108 : 1],
[-10 : 4 : 1]
2.08355504234802,
2.13825066196826,
2.16335833290499
[-10, 4], [2, 32], [17, 77], [22, 108], [25, 129], [1330, 48504], [6194, 487480] 1016
1017 [0, 0, 0, 0, 1017]
0
12411468
{O}
-
0 - - - 1017
1018 [0, 0, 0, 0, 1018]
0
149230656
{O}
-
1 [-9 : 17 : 1] 2.84448128740334
[-9, 17] 1018
1019 [0, 0, 0, 0, 1019]
0
448571952
{O}
-
1 [-7 : 26 : 1] 2.82080481338197
[-7, 26] 1019
1020 [0, 0, 0, 0, 1020]
0
28090800
{O}
-
1 [-1978 : 388582 : 12167] 8.34916509284717
- 1020
1021 [0, 0, 0, 0, 1021]
0
112583628
{O}
-
0 - - - 1021
1022 [0, 0, 0, 0, 1022]
0
451217088
{O}
-
0 - - - 1022
1023 [0, 0, 0, 0, 1023]
0
452100528
{O}
-
2 [1 : 32 : 1],
[4 : 2047 : 64]
2.77385852107556,
5.54485770017458
[1, 32], [4657, 317804] 1023
1024 [0, 0, 0, 0, 1024]
0
27
Z/3Z
[0, 32]
0 - - [0, 32] 1024
1025 [0, 0, 0, 0, 1025]
0
1512900
{O}
-
3 [-5 : 30 : 1],
[-10 : 5 : 1],
[-4 : 31 : 1]
1.17906048434744,
1.32401434115313,
2.33008392335451
[-10, 5], [-5, 30], [-4, 31], [-1, 32], [4, 33], [10, 45], [20, 95], [40, 255], [50, 355], [64, 513], [155, 1930], [166, 2139], [446, 9419], [920, 27905], [3631, 218796], [3730, 227805] 1025
1026 [0, 0, 0, 0, 1026]
0
623808
{O}
-
1 [7 : 37 : 1] 2.86704240622118
[7, 37] 1026
1027 [0, 0, 0, 0, 1027]
0
151880976
{O}
-
1 [5797 : 157572 : 4913] 7.89291973050336
- 1027
1028 [0, 0, 0, 0, 1028]
0
7133292
{O}
-
0 - - - 1028
1029 [0, 0, 0, 0, 1029]
0
47628
{O}
-
0 - - - 1029
1030 [0, 0, 0, 0, 1030]
0
458308800
{O}
-
1 [51706626 : -271740913 : 7301384] 13.4060517796508
- 1030
1031 [0, 0, 0, 0, 1031]
0
459199152
{O}
-
2 [5 : 34 : 1],
[1508 : 7603 : 64]
2.82114642246154,
6.20328039577566
[5, 34] 1031
1032 [0, 0, 0, 0, 1032]
0
28755648
{O}
-
2 [-2 : 32 : 1],
[814 : 23224 : 1]
2.08742194605419,
6.01644871270464
[-2, 32], [814, 23224] 1032
1033 [0, 0, 0, 0, 1033]
0
115245612
{O}
-
1 [14364 : 93605 : 343] 7.31450098705975
- 1033
1034 [0, 0, 0, 0, 1034]
0
153958464
{O}
-
1 [-2154 : 1405 : 216] 6.44478282270800
- 1034
1035 [0, 0, 0, 0, 1035]
0
51418800
{O}
-
2 [9 : 42 : 1],
[1156 : 5327 : 64]
2.19731264431483,
6.02486442928428
[9, 42] 1035
1036 [0, 0, 0, 0, 1036]
0
9659664
{O}
-
1 [-10 : 6 : 1] 1.61972477351314
[-10, 6], [645, 16381] 1036
1037 [0, 0, 0, 0, 1037]
0
116139852
{O}
-
0 - - - 1037
1038 [0, 0, 0, 0, 1038]
0
465455808
{O}
-
1 [-92 : 2059 : 64] 5.55256654758190
- 1038
1039 [0, 0, 0, 0, 1039]
0
466353072
{O}
-
1 [-59793 : -133094 : 6859] 8.73593887899027
- 1039
1040 [0, 0, 0, 0, 1040]
0
114075
{O}
-
0 - - - 1040
1041 [0, 0, 0, 0, 1041]
0
117037548
{O}
-
1 [-8 : 23 : 1] 2.37688459433518
[-8, 23] 1041
1042 [0, 0, 0, 0, 1042]
0
469050048
{O}
-
0 - - - 1042
1043 [0, 0, 0, 0, 1043]
0
156650256
{O}
-
1 [-572 : 1161 : 64] 5.07418205191504
- 1043
1044 [0, 0, 0, 0, 1044]
0
817452
{O}
-
0 - - - 1044
1045 [0, 0, 0, 0, 1045]
0
39312900
{O}
-
0 - - - 1045
1046 [0, 0, 0, 0, 1046]
0
472658112
{O}
-
1 [993 : 6085 : 27] 5.97414725255533
- 1046
1047 [0, 0, 0, 0, 1047]
0
473562288
{O}
-
1 [-35457512924239 : 509469739842454 : 15830267370029] 23.0485597128442
- 1047
1048 [0, 0, 0, 0, 1048]
0
29654208
{O}
-
1 [1284 : 6113 : 64] 6.09389564253065
- 1048
1049 [0, 0, 0, 0, 1049]
0
118843308
{O}
-
1 [-10 : 7 : 1] 2.40371211226293
[-10, 7] 1049
1050 [0, 0, 0, 0, 1050]
0
19051200
{O}
-
1 [7431918 : 33188329 : 474552] 11.8830528027409
- 1050
1051 [0, 0, 0, 0, 1051]
0
477187632
{O}
-
2 [-3 : 32 : 1],
[8895 : 161452 : 27]
2.79257723450795,
8.01361666021502
[-3, 32] 1051
1052 [0, 0, 0, 0, 1052]
0
9960336
{O}
-
1 [13 : 57 : 1] 2.52429524893011
[13, 57] 1052
1053 [0, 0, 0, 0, 1053]
0
164268
{O}
-
2 [-9 : 18 : 1],
[27 : 144 : 1]
1.38968067556157,
2.06802827286468
[-9, 18], [27, 144] 1053
1054 [0, 0, 0, 0, 1054]
0
159971904
{O}
-
1 [-96460 : 4564191 : 140608] 10.1360685244025
- 1054
1055 [0, 0, 0, 0, 1055]
0
480826800
{O}
-
1 [392992 : -1727731 : 32768] 9.96915199875842
- 1055
1056 [0, 0, 0, 0, 1056]
0
1881792
{O}
-
1 [3423407 : 15728083 : 357911] 11.4783895081919
- 1056
1057 [0, 0, 0, 0, 1057]
0
120662892
{O}
-
2 [-6 : 29 : 1],
[18 : 83 : 1]
2.35904281266253,
2.79067634348493
[-6, 29], [18, 83] 1057
1058 [0, 0, 0, 0, 1058]
0
914112
{O}
-
1 [23 : 115 : 1] 1.32562007627849
[23, 115] 1058
1059 [0, 0, 0, 0, 1059]
0
484479792
{O}
-
0 - - - 1059
1060 [0, 0, 0, 0, 1060]
0
7584300
{O}
-
1 [24 : 122 : 1] 2.52232214849007
[24, 122] 1060
1061 [0, 0, 0, 0, 1061]
0
40525956
{O}
-
0 - - - 1061
1062 [0, 0, 0, 0, 1062]
0
54136512
{O}
-
2 [3 : 33 : 1],
[19 : 89 : 1]
2.06763690773336,
3.28741277983508
[3, 33], [19, 89] 1062
1063 [0, 0, 0, 0, 1063]
0
162715536
{O}
-
1 [-120484 : 657705 : 21952] 8.93276173231857
- 1063
1064 [0, 0, 0, 0, 1064]
0
30566592
{O}
-
1 [-10 : 8 : 1] 2.17680165552940
[-10, 8] 1064
1065 [0, 0, 0, 0, 1065]
0
122496300
{O}
-
0 - - - 1065
1066 [0, 0, 0, 0, 1066]
0
490905792
{O}
-
1 [444192 : -1954285 : 32768] 10.0275133120995
- 1066
1067 [0, 0, 0, 0, 1067]
0
491827248
{O}
-
0 - - - 1067
1068 [0, 0, 0, 0, 1068]
0
30796848
{O}
-
0 - - - 1068
1069 [0, 0, 0, 0, 1069]
0
123418188
{O}
-
1 [687648 : -3327305 : 32768] 10.2850553737510
- 1069
1070 [0, 0, 0, 0, 1070]
0
164865600
{O}
-
1 [11 : 49 : 1] 3.00512912719821
[11, 49] 1070
1071 [0, 0, 0, 0, 1071]
0
55057968
{O}
-
1 [-5176 : 3149 : 512] 7.03211146372585
- 1071
1072 [0, 0, 0, 0, 1072]
0
646416
{O}
-
1 [-7 : 27 : 1] 2.28706202889638
[-7, 27] 1072
1073 [0, 0, 0, 0, 1073]
0
124343532
{O}
-
0 - - - 1073
1074 [0, 0, 0, 0, 1074]
0
498301632
{O}
-
1 [-123 : 845 : 27] 5.00925739060525
- 1074
1075 [0, 0, 0, 0, 1075]
0
19969200
{O}
-
0 - - - 1075
1076 [0, 0, 0, 0, 1076]
0
7814988
{O}
-
1 [59475 : 1946719 : 59319] 10.1177729971421
- 1076
1077 [0, 0, 0, 0, 1077]
0
125272332
{O}
-
1 [7308150 : 111280519 : 3375000] 12.8183087012600
- 1077
1078 [0, 0, 0, 0, 1078]
0
10245312
{O}
-
0 - - - 1078
1079 [0, 0, 0, 0, 1079]
0
167650704
{O}
-
1 [50 : 291 : 8] 3.69871633611116
- 1079
1080 [0, 0, 0, 0, 1080]
0
43200
{O}
-
1 [6 : 36 : 1] 0.69816982375727
[6, 36] 1080
1081 [0, 0, 0, 0, 1081]
0
42068196
{O}
-
2 [2 : 33 : 1],
[-10 : 9 : 1]
1.78568448900789,
1.86316904378426
[-10, 9], [2, 33], [12, 53] 1081
1082 [0, 0, 0, 0, 1082]
0
505752768
{O}
-
1 [6315631511254541 : 58075001111524231 : 74826025131619] 25.8081013460324
- 1082
1083 [0, 0, 0, 0, 1083]
0
1403568
{O}
-
1 [146 : 677 : 8] 4.65070216646774
- 1083
1084 [0, 0, 0, 0, 1084]
0
31726512
{O}
-
1 [111 : 917 : 27] 5.01826284170273
- 1084
1085 [0, 0, 0, 0, 1085]
0
127140300
{O}
-
1 [63709843244 : -1226597975903 : 171879616] 18.5738891132029
- 1085
1086 [0, 0, 0, 0, 1086]
0
509499072
{O}
-
2 [-5 : 31 : 1],
[36878475 : -278911619 : 8120601]
2.81967170363634,
13.4351651370636
[-5, 31] 1086
1087 [0, 0, 0, 0, 1087]
0
510437808
{O}
-
0 - - - 1087
1088 [0, 0, 0, 0, 1088]
0
10404
{O}
-
2 [-8 : 24 : 1],
[-4 : 32 : 1]
0.45461686518421,
1.42510431540567
[-8, 24], [-4, 32], [1, 33], [8, 40], [16, 72], [32, 184], [172, 2256], [208, 3000], [20936, 3029288] 1088
1089 [0, 0, 0, 0, 1089]
0
117612
Z/3Z
[0, 33]
0 - - [0, 33] 1089
1090 [0, 0, 0, 0, 1090]
0
171086400
{O}
-
3 [-1 : 33 : 1],
[-9 : 19 : 1],
[4473 : 19727 : 343]
2.24547852800417,
2.86474779593861,
6.97316233145292
[-9, 19], [-1, 33], [28187351, 149651610621] 1090
1091 [0, 0, 0, 0, 1091]
0
514201392
{O}
-
1 [-407540730 : 51290207423 : 1552836312] 16.9027126499057
- 1091
1092 [0, 0, 0, 0, 1092]
0
8049132
{O}
-
2 [4 : 34 : 1],
[242 : 1357 : 8]
1.89747924733913,
5.00918202380911
[4, 34], [918493, 880265693] 1092
1093 [0, 0, 0, 0, 1093]
0
129022092
{O}
-
0 - - - 1093
1094 [0, 0, 0, 0, 1094]
0
517033152
{O}
-
0 - - - 1094
1095 [0, 0, 0, 0, 1095]
0
517978800
{O}
-
0 - - - 1095
1096 [0, 0, 0, 0, 1096]
0
32432832
{O}
-
0 - - - 1096
1097 [0, 0, 0, 0, 1097]
0
43322724
{O}
-
2 [-2 : 33 : 1],
[34 : 201 : 1]
1.78932206839523,
2.70446298980843
[-2, 33], [34, 201] 1097
1098 [0, 0, 0, 0, 1098]
0
57868992
{O}
-
1 [-2564023793454 : 6062019334903 : 293019561288] 20.4662628226341
- 1098
1099 [0, 0, 0, 0, 1099]
0
173923344
{O}
-
1 [4905 : 31004 : 125] 7.05230803706824
- 1099
1100 [0, 0, 0, 0, 1100]
0
1306800
{O}
-
2 [-10 : 10 : 1],
[5 : 35 : 1]
1.11355561824154,
1.76771032765662
[-10, 10], [5, 35], [14, 62], [245, 3835] 1100
1101 [0, 0, 0, 0, 1101]
0
130917708
{O}
-
2 [7 : 38 : 1],
[20510 : 106931 : 2744]
2.88614938433978,
8.17705816207471
[7, 38], [26299, 4264900] 1101
1102 [0, 0, 0, 0, 1102]
0
524622528
{O}
-
1 [-159 : 809 : 27] 5.03025545530614
- 1102
1103 [0, 0, 0, 0, 1103]
0
525575088
{O}
-
2 [651 : 3320 : 27],
[448735 : 2033494 : 42875]
5.65078726735088,
10.1037395188752
- 1103
1104 [0, 0, 0, 0, 1104]
0
128547
{O}
-
0 - - - 1104
1105 [0, 0, 0, 0, 1105]
0
131870700
{O}
-
1 [15534 : 75691 : 729] 7.29984888531593
- 1105
1106 [0, 0, 0, 0, 1106]
0
176145984
{O}
-
1 [239 : 3695 : 1] 5.50308597029760
[239, 3695] 1106
1107 [0, 0, 0, 0, 1107]
0
726192
{O}
-
0 - - - 1107
1108 [0, 0, 0, 0, 1108]
0
2762244
{O}
-
0 - - - 1108
1109 [0, 0, 0, 0, 1109]
0
132827148
{O}
-
0 - - - 1109
1110 [0, 0, 0, 0, 1110]
0
532267200
{O}
-
1 [-4075575 : -6090173 : 421875] 11.5131227016910
- 1110
1111 [0, 0, 0, 0, 1111]
0
533226672
{O}
-
1 [76190610 : -1918990789 : 57512456] 14.7141332831425
- 1111
1112 [0, 0, 0, 0, 1112]
0
33386688
{O}
-
0 - - - 1112
1113 [0, 0, 0, 0, 1113]
0
133787052
{O}
-
1 [-186 : 757 : 27] 4.58181916578370
- 1113
1114 [0, 0, 0, 0, 1114]
0
536110272
{O}
-
2 [15 : 67 : 1],
[3318 : 14869 : 216]
3.15500660972706,
6.75131596246081
[15, 67], [141471, 53210965] 1114
1115 [0, 0, 0, 0, 1115]
0
179024400
{O}
-
1 [24557 : 110102 : 2197] 8.14963967330650
- 1115
1116 [0, 0, 0, 0, 1116]
0
3736368
{O}
-
2 [-6 : 30 : 1],
[-3 : 33 : 1]
1.41256375581506,
2.07976556002477
[-6, 30], [-3, 33], [10, 46], [450, 9546] 1116
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1 [2466421792 : -676668649681 : 32768] 18.1603964562761
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1 [-11 : 20 : 1] 3.02412848448085
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2 [37 : 229 : 1],
[-94 : 103 : 8]
3.81631160209645,
4.42780333434687
[37, 229] 1788
1789 [0, 0, 0, 0, 1789]
0
345656268
{O}
-
1 [-36102384870737955 : 212938697160911056 : 5489685226091143] 27.1526823228409
- 1789
1790 [0, 0, 0, 0, 1790]
0
461390400
{O}
-
1 [19 : 93 : 1] 2.80686486166512
[19, 93] 1790
1791 [0, 0, 0, 0, 1791]
0
153968688
{O}
-
2 [-3 : 42 : 1],
[20745 : 114884 : 729]
2.23468871497367,
8.01256206744359
[-3, 42] 1791
1792 [0, 0, 0, 0, 1792]
0
7056
{O}
-
1 [8 : -48 : 1] 0.41462415202842
[-12, 8], [8, 48], [753, 20663] 1792
1793 [0, 0, 0, 0, 1793]
0
347203692
{O}
-
0 - - - 1793
1794 [0, 0, 0, 0, 1794]
0
1390364352
{O}
-
1 [2195 : 10613 : 125] 6.53204422419173
- 1794
1795 [0, 0, 0, 0, 1795]
0
1391914800
{O}
-
1 [7649340 : -46431487 : 216000] 11.9709597862130
- 1795
1796 [0, 0, 0, 0, 1796]
0
21772908
{O}
-
1 [77 : 677 : 1] 4.44136310401528
[77, 677] 1796
1797 [0, 0, 0, 0, 1797]
0
348754572
{O}
-
1 [3233709460020 : 17355094413193 : 123505992000] 20.5860177859905
- 1797
1798 [0, 0, 0, 0, 1798]
0
1396571328
{O}
-
0 - - - 1798
1799 [0, 0, 0, 0, 1799]
0
466041744
{O}
-
1 [25 : 132 : 1] 2.97882695693489
[25, 132] 1799
1800 [0, 0, 0, 0, 1800]
0
388800
{O}
-
0 - - - 1800
1801 [0, 0, 0, 0, 1801]
0
116769636
{O}
-
2 [20 : 99 : 1],
[24 : 125 : 1]
2.37531030358305,
3.03884457612361
[20, 99], [24, 125], [3092, 171933] 1801
1802 [0, 0, 0, 0, 1802]
0
1402792128
{O}
-
1 [47 : 325 : 1] 4.01129207920061
[47, 325] 1802
1803 [0, 0, 0, 0, 1803]
0
1404349488
{O}
-
1 [19558 : 452909 : 10648] 9.14703686008561
- 1803
1804 [0, 0, 0, 0, 1804]
0
87869232
{O}
-
1 [390 : 7702 : 1] 5.29220067817190
[390, 7702] 1804
1805 [0, 0, 0, 0, 1805]
0
974700
{O}
-
1 [11 : 56 : 1] 3.11965402637496
[11, 56] 1805
1806 [0, 0, 0, 0, 1806]
0
1409026752
{O}
-
2 [-5 : 41 : 1],
[-6130469370 : 64857040417 : 1552836312]
2.98219211081022,
17.0840461263000
[-5, 41] 1806
1807 [0, 0, 0, 0, 1807]
0
1410587568
{O}
-
0 - - - 1807
1808 [0, 0, 0, 0, 1808]
0
114921
{O}
-
1 [-8 : 36 : 1] 1.07190475523891
[-8, 36] 1808
1809 [0, 0, 0, 0, 1809]
0
484812
{O}
-
2 [6 : 45 : 1],
[-12 : 9 : 1]
1.08114997738081,
1.12062647888794
[-12, 9], [6, 45], [10, 53], [15, 72], [148, 1801], [600, 14697] 1809
1810 [0, 0, 0, 0, 1810]
0
471758400
{O}
-
1 [64484 : 2046861 : 64] 9.14601106066259
- 1810
1811 [0, 0, 0, 0, 1811]
0
1416839472
{O}
-
3 [5 : 44 : 1],
[17 : 82 : 1],
[-52534940 : 48626839 : 4410944]
2.99370054460106,
3.29771163657033,
13.2466534248053
1811
1812 [0, 0, 0, 0, 1812]
0
22162572
{O}
-
0 - - - 1812
1813 [0, 0, 0, 0, 1813]
0
7244748
{O}
-
0 - - - 1813
1814 [0, 0, 0, 0, 1814]
0
1421537472
{O}
-
0 - - - 1814
1815 [0, 0, 0, 0, 1815]
0
11761200
{O}
-
1 [-11 : 22 : 1] 1.43952393004881
[-11, 22] 1815
1816 [0, 0, 0, 0, 1816]
0
89042112
{O}
-
2 [-6 : 40 : 1],
[222 : 3308 : 1]
2.29842369249440,
4.74335086149348
[-6, 40], [222, 3308] 1816
1817 [0, 0, 0, 0, 1817]
0
118853604
{O}
-
0 - - - 1817
1818 [0, 0, 0, 0, 1818]
0
158645952
{O}
-
2 [-9 : 33 : 1],
[306 : 1923 : 8]
2.28623596467801,
4.49765364455501
[-9, 33] 1818
1819 [0, 0, 0, 0, 1819]
0
476461584
{O}
-
1 [-835705 : 2039016 : 79507] 10.0068766368887
- 1819
1820 [0, 0, 0, 0, 1820]
0
89434800
{O}
-
1 [74 : 638 : 1] 3.71292319395197
[74, 638] 1820
1821 [0, 0, 0, 0, 1821]
0
358132428
{O}
-
0 - - - 1821
1822 [0, 0, 0, 0, 1822]
0
1434103488
{O}
-
1 [3 : 43 : 1] 2.97513217066695
[3, 43] 1822
1823 [0, 0, 0, 0, 1823]
0
1435678128
{O}
-
0 - - - 1823
1824 [0, 0, 0, 0, 1824]
0
5614272
{O}
-
0 - - - 1824
1825 [0, 0, 0, 0, 1825]
0
14388300
{O}
-
0 - - - 1825
1826 [0, 0, 0, 0, 1826]
0
480135744
{O}
-
1 [-111724580 : 275789409 : 10648000] 13.2726877246201
- 1826
1827 [0, 0, 0, 0, 1827]
0
160220592
{O}
-
1 [21416839952029 : -164981762064946 : 364147304221] 21.9504578321308
- 1827
1828 [0, 0, 0, 0, 1828]
0
7518564
{O}
-
2 [-4 : 42 : 1],
[-12 : 10 : 1]
1.50590253712344,
2.12638962838261
[-12, 10], [-4, 42], [32, 186] 1828
1829 [0, 0, 0, 0, 1829]
0
361286028
{O}
-
0 - - - 1829
1830 [0, 0, 0, 0, 1830]
0
1446724800
{O}
-
1 [-10932 : 68617 : 1728] 7.96646061377540
- 1830
1831 [0, 0, 0, 0, 1831]
0
1448306352
{O}
-
1 [4556068965 : 150538271654 : 4173281] 17.1652137455894
- 1831
1832 [0, 0, 0, 0, 1832]
0
90618048
{O}
-
0 - - - 1832
1833 [0, 0, 0, 0, 1833]
0
362868012
{O}
-
1 [16 : 77 : 1] 2.80736796687620
[16, 77] 1833
1834 [0, 0, 0, 0, 1834]
0
1453056192
{O}
-
2 [1158 : 9631 : 216],
[-22269 : 61853 : 2197]
6.58607217699890,
8.16235785754598
- 1834
1835 [0, 0, 0, 0, 1835]
0
484880400
{O}
-
1 [41 : 266 : 1] 3.90004475056169
[41, 266] 1835
1836 [0, 0, 0, 0, 1836]
0
124848
{O}
-
0 - - - 1836
1837 [0, 0, 0, 0, 1837]
0
121484484
{O}
-
0 - - - 1837
1838 [0, 0, 0, 0, 1838]
0
1459401408
{O}
-
1 [-56704783086913311 : 236568362626070137 : 6723338063827419] 27.3128486833859
- 1838
1839 [0, 0, 0, 0, 1839]
0
1460989872
{O}
-
1 [194050045 : -7880914042 : 117649] 15.1963747347792
- 1839
1840 [0, 0, 0, 0, 1840]
0
5713200
{O}
-
1 [25868223 : 477327319 : 11089567] 13.7884175438835
- 1840
1841 [0, 0, 0, 0, 1841]
0
366042348
{O}
-
3 [2 : 43 : 1],
[-10 : 29 : 1],
[444 : 2141 : 27]
2.51047289340467,
2.57014663404495,
5.01875275523007
[-10, 29],[2, 43], [44, 295] 1841
1842 [0, 0, 0, 0, 1842]
0
1465760448
{O}
-
0 - - - 1842
1843 [0, 0, 0, 0, 1843]
0
1467352368
{O}
-
0 - - - 1843
1844 [0, 0, 0, 0, 1844]
0
7650756
{O}
-
0 - - - 1844
1845 [0, 0, 0, 0, 1845]
0
40848300
{O}
-
1 [2457 : 16134 : 343] 6.19387277044482
- 1845
1846 [0, 0, 0, 0, 1846]
0
490711104
{O}
-
1 [4267 : 211125 : 4913] 8.08694435187542
- 1846
1847 [0, 0, 0, 0, 1847]
0
1473728688
{O}
-
1 [-16519353 : -12588940 : 1367631] 12.4734825675408
- 1847
1848 [0, 0, 0, 0, 1848]
0
92207808
{O}
-
1 [1 : 43 : 1] 2.97045048988385
[1, 43] 1848
1849 [0, 0, 0, 0, 1849]
0
199692
Z/3Z
[0, 43]
2 [-12 : 11 : 1],
[126 : 1415 : 1]
2.59181864970913,
4.43420883977263
[-12, 11], [0, 43], [126, 1415] 1849
1850 [0, 0, 0, 0, 1850]
0
59140800
{O}
-
1 [-1 : 43 : 1] 2.97072044635241
[-1, 43] 1850
1851 [0, 0, 0, 0, 1851]
0
1480118832
{O}
-
2 [-94 : 121 : 8],
[349 : 6520 : 1]
4.43793176864753,
5.87671470034869
[349, 6520] 1851
1852 [0, 0, 0, 0, 1852]
0
92607408
{O}
-
0 - - - 1852
1853 [0, 0, 0, 0, 1853]
0
123609924
{O}
-
0 - - - 1853
1854 [0, 0, 0, 0, 1854]
0
164991168
{O}
-
1 [777029895525 : -22498333596487 : 926859375] 20.5053198969851
- 1854
1855 [0, 0, 0, 0, 1855]
0
495507600
{O}
-
1 [29 : 162 : 1] 3.08569965999002
[29, 162] 1855
1856 [0, 0, 0, 0, 1856]
0
90828
{O}
-
0 - - - 1856
1857 [0, 0, 0, 0, 1857]
0
372432492
{O}
-
2 [-2 : 43 : 1],
[1218 : 8263 : 27]
2.51262151636166,
5.71402767696574
[-2, 43] 1857
1858 [0, 0, 0, 0, 1858]
0
1491334848
{O}
-
1 [-282 : 9305 : 216] 6.55633706418896
- 1858
1859 [0, 0, 0, 0, 1859]
0
8833968
{O}
-
0 - - - 1859
1860 [0, 0, 0, 0, 1860]
0
23352300
{O}
-
1 [-11 : 23 : 1] 3.04536645677711
[-11, 23] 1860
1861 [0, 0, 0, 0, 1861]
0
374038668
{O}
-
1 [-1787997 : -13543838 : 328509] 11.4632707895835
- 1861
1862 [0, 0, 0, 0, 1862]
0
10188864
{O}
-
1 [1922 : 29793 : 8] 6.35017892114114
- 1862
1863 [0, 0, 0, 0, 1863]
0
2056752
{O}
-
0 - - - 1863
1864 [0, 0, 0, 0, 1864]
0
31270464
{O}
-
1 [-7 : 39 : 1] 2.45878264874513
[-7, 39] 1864
1865 [0, 0, 0, 0, 1865]
0
375648300
{O}
-
0 - - - 1865
1866 [0, 0, 0, 0, 1866]
0
1504204992
{O}
-
1 [7 : 47 : 1] 3.03464400347995
[7, 47] 1866
1867 [0, 0, 0, 0, 1867]
0
1505817648
{O}
-
1 [264594 : 12424949 : 287496] 11.3529972923596
- 1867
1868 [0, 0, 0, 0, 1868]
0
94214448
{O}
-
0 - - - 1868
1869 [0, 0, 0, 0, 1869]
0
377261388
{O}
-
1 [968900622495 : -4766413913162 : 50858627625] 19.7988176852974
- 1869
1870 [0, 0, 0, 0, 1870]
0
1510660800
{O}
-
2 [18 : 347 : 8],
[-303 : 577 : 27]
4.36525067475811,
5.24643942238741
- 1870
1871 [0, 0, 0, 0, 1871]
0
504092304
{O}
-
1 [219 : 1324 : 27] 5.25487477244467
- 1871
1872 [0, 0, 0, 0, 1872]
0
41067
{O}
-
2 [-12 : 12 : 1],
[4 : 44 : 1]
0.93882168640164,
1.60626684323812
[-12, 12], [4, 44], [9, 51], [12, 60], [153, 1893], [348, 6492], [1348, 49492] 1872
1873 [0, 0, 0, 0, 1873]
0
126292644
{O}
-
0 - - - 1873
1874 [0, 0, 0, 0, 1874]
0
1517130432
{O}
-
1 [3689 : 19153 : 343] 7.01372061063327
- 1874
1875 [0, 0, 0, 0, 1875]
0
97200
{O}
-
0 - - - 1875
1876 [0, 0, 0, 0, 1876]
0
23755788
{O}
-
2 [-3 : 43 : 1],
[18888 : 116845 : 512]
2.98232206287469,
7.97628956175381
[-3, 43] 1876
1877 [0, 0, 0, 0, 1877]
0
380497932
{O}
-
1 [-2779 : 12580 : 343] 6.91182408927328
- 1877
1878 [0, 0, 0, 0, 1878]
0
1523613888
{O}
-
0 - - - 1878
1879 [0, 0, 0, 0, 1879]
0
1525236912
{O}
-
0 - - - 1879
1880 [0, 0, 0, 0, 1880]
0
31809600
{O}
-
1 [14 : 68 : 1] 2.52112896266794
[14, 68] 1880
1881 [0, 0, 0, 0, 1881]
0
42457932
{O}
-
2 [-8 : 37 : 1],
[115 : 1234 : 1]
2.55763576406128,
4.81110206627501
[-8, 37], [115, 1234] 1881
1882 [0, 0, 0, 0, 1882]
0
510037056
{O}
-
1 [68678571 : 598201415 : 13312053] 13.9438872118435
- 1882
1883 [0, 0, 0, 0, 1883]
0
1531737648
{O}
-
1 [3262 : 119125 : 2744] 8.25525223187446
- 1883
1884 [0, 0, 0, 0, 1884]
0
95835312
{O}
-
1 [-330 : 206 : 27] 4.56576691072430
- 1884
1885 [0, 0, 0, 0, 1885]
0
383748300
{O}
-
2 [-9 : 34 : 1],
[12864720 : 68209877 : 512000]
3.02966898313679,
12.3006545890470
[-9, 34] 1885
1886 [0, 0, 0, 0, 1886]
0
1536622272
{O}
-
0 - - - 1886
1887 [0, 0, 0, 0, 1887]
0
1538252208
{O}
-
2 [-2583 : 31292 : 729],
[1181124 : -6278869 : 46656]
7.38153045472834,
10.7088095680249
- 1887
1888 [0, 0, 0, 0, 1888]
0
6015168
{O}
-
0 - - - 1888
1889 [0, 0, 0, 0, 1889]
0
128459556
{O}
-
2 [-5 : 42 : 1],
[8 : 49 : 1]
2.44733071965007,
2.59584400052083
[-5, 42], [8, 49], [46, 315] 1889
1890 [0, 0, 0, 0, 1890]
0
2116800
{O}
-
0 - - - 1890
1891 [0, 0, 0, 0, 1891]
0
514926864
{O}
-
1 [-30 : 343 : 8] 4.37523856034537
- 1891
1892 [0, 0, 0, 0, 1892]
0
24162732
{O}
-
0 - - - 1892
1893 [0, 0, 0, 0, 1893]
0
387012492
{O}
-
2 [31 : 178 : 1],
[5384 : 28303 : 512]
3.68552311938161,
7.27692358708003
[31, 178] 1893
1894 [0, 0, 0, 0, 1894]
0
1549685952
{O}
-
1 [3693501 : 17886527 : 250047] 11.5247826804009
- 1894
1895 [0, 0, 0, 0, 1895]
0
1551322800
{O}
-
0 - - - 1895
1896 [0, 0, 0, 0, 1896]
0
97060032
{O}
-
2 [22 : 112 : 1],
[21910 : -175748 : 343]
2.75805974885394,
7.47565137489502
[22, 112] 1896
1897 [0, 0, 0, 0, 1897]
0
388649772
{O}
-
3 [-6 : 41 : 1],
[-12 : 13 : 1],
[228 : 3443 : 1]
2.54332821651127,
2.59930020150860,
5.00066015937729
[-12, 13], [-6, 41], [99, 986], [228, 3443] 1897
1898 [0, 0, 0, 0, 1898]
0
518746176
{O}
-
1 [98 : 489 : 8] 4.00270803996145
- 1898
1899 [0, 0, 0, 0, 1899]
0
173097648
{O}
-
2 [13 : 64 : 1],
[201 : 2850 : 1]
3.18717201603652,
4.60881751171048
[13, 64], [201, 2850] 1899
1900 [0, 0, 0, 0, 1900]
0
1299600
{O}
-
2 [-10 : 30 : 1],
[5 : 45 : 1]
0.72630977809896,
1.38638820935939
[-10, 30], [5, 45], [6, 46], [30, 170], [45, 305], [8270, 752070] 1900
1901 [0, 0, 0, 0, 1901]
0
390290508
{O}
-
2 [-231 : 964 : 27],
[34540854390 : -192698216947 : 1197770328]
5.22530969434311,
17.5690788740040
- 1901
1902 [0, 0, 0, 0, 1902]
0
1562804928
{O}
-
1 [-46 : 331 : 8] 4.39062770895911
- 1902
1903 [0, 0, 0, 0, 1903]
0
1564448688
{O}
-
1 [-2880927546312 : 30758217182749 : 717398097408] 21.1918408676805
- 1903
1904 [0, 0, 0, 0, 1904]
0
6117552
{O}
-
0 - - - 1904
1905 [0, 0, 0, 0, 1905]
0
391934700
{O}
-
1 [34 : 203 : 1] 3.29333108128937
[34, 203] 1905
1906 [0, 0, 0, 0, 1906]
0
1569385152
{O}
-
0 - - - 1906
1907 [0, 0, 0, 0, 1907]
0
523677456
{O}
-
3 [-11 : 24 : 1],
[82 : 437 : 8],
[113 : 1202 : 1]
2.50345288190806,
4.49930215467795,
4.79504455983249
[-11, 24], [113, 1202], [2993, 163742] 1907
1908 [0, 0, 0, 0, 1908]
0
2730348
{O}
-
0 - - - 1908
1909 [0, 0, 0, 0, 1909]
0
131194116
{O}
-
2 [3 : 44 : 1],
[131 : 1500 : 1]
2.99034322538721,
4.38423709697142
[3, 44], [131, 1500] 1909
1910 [0, 0, 0, 0, 1910]
0
1575979200
{O}
-
1 [-4111888606741313697 : -2683282166428630571 : 335199796985983077] 29.9684779405021
- 1910
1911 [0, 0, 0, 0, 1911]
0
32196528
{O}
-
1 [-105 : 1162 : 27] 3.89313496392225
- 1911
1912 [0, 0, 0, 0, 1912]
0
98705088
{O}
-
1 [18 : 88 : 1] 2.64312603087728
[18, 88] 1912
1913 [0, 0, 0, 0, 1913]
0
395233452
{O}
-
1 [-4 : 43 : 1] 2.53208779645793
[-4, 43] 1913
1914 [0, 0, 0, 0, 1914]
0
1582587072
{O}
-
0 - - - 1914
1915 [0, 0, 0, 0, 1915]
0
1584241200
{O}
-
0 - - - 1915
1916 [0, 0, 0, 0, 1916]
0
33039504
{O}
-
1 [10 : 54 : 1] 1.86541995549524
[10, 54] 1916
1917 [0, 0, 0, 0, 1917]
0
181476
{O}
-
1 [228 : 2835 : 64] 4.12079486299785
- 1917
1918 [0, 0, 0, 0, 1918]
0
529736256
{O}
-
1 [11 : 57 : 1] 2.58459060122292
[11, 57] 1918
1919 [0, 0, 0, 0, 1919]
0
1590866352
{O}
-
1 [-62 : 305 : 8] 4.40998586972951
- 1919
1920 [0, 0, 0, 0, 1920]
0
388800
{O}
-
1 [76 : 664 : 1] 3.04553796383648
[76, 664] 1920
1921 [0, 0, 0, 0, 1921]
0
398546028
{O}
-
0 - - - 1921
1922 [0, 0, 0, 0, 1922]
0
1660608
{O}
-
0 - - - 1922
1923 [0, 0, 0, 0, 1923]
0
1597505328
{O}
-
2 [292 : 2875 : 64],
[-21585 : 137566 : 3375]
5.77972837260035,
8.42897934397694
- 1923
1924 [0, 0, 0, 0, 1924]
0
24986988
{O}
-
1 [-12 : 14 : 1] 2.14133239188351
[-12, 14] 1924
1925 [0, 0, 0, 0, 1925]
0
5336100
{O}
-
1 [2 : 351 : 8] 3.82004286192820
- 1925
1926 [0, 0, 0, 0, 1926]
0
178054848
{O}
-
2 [27 : 147 : 1],
[75 : 651 : 1]
2.85564134893998,
3.68764779208360
[27, 147], [75, 651] 1926
1927 [0, 0, 0, 0, 1927]
0
534719376
{O}
-
1 [-78 : 253 : 8] 4.42983394865927
- 1927
1928 [0, 0, 0, 0, 1928]
0
100363968
{O}
-
1 [2 : 44 : 1] 2.29467518457874
[2, 44] 1928
1929 [0, 0, 0, 0, 1929]
0
401872428
{O}
-
0 - - - 1929
1930 [0, 0, 0, 0, 1930]
0
1609156800
{O}
-
1 [7752 : 37627 : 512] 7.41183348552019
- 1930
1931 [0, 0, 0, 0, 1931]
0
1610824752
{O}
-
0 - - - 1931
1932 [0, 0, 0, 0, 1932]
0
100780848
{O}
-
0 - - - 1932
1933 [0, 0, 0, 0, 1933]
0
403540812
{O}
-
1 [287898 : 1398145 : 17576] 9.80616648659709
- 1933
1934 [0, 0, 0, 0, 1934]
0
538611264
{O}
-
1 [283 : 4761 : 1] 5.12322803046433
[283, 4761] 1934
1935 [0, 0, 0, 0, 1935]
0
179722800
{O}
-
1 [1 : 44 : 1] 2.98575208663612
[1, 44] 1935
1936 [0, 0, 0, 0, 1936]
0
1089
Z/3Z
[0, 44]
0 - - [0, 44] 1936
1937 [0, 0, 0, 0, 1937]
0
405212652
{O}
-
2 [-1 : 44 : 1],
[34 : 359 : 8]
2.98600992505673,
4.39231431784772
[-1, 44] 1937
1938 [0, 0, 0, 0, 1938]
0
1622524608
{O}
-
1 [2219194144 : -10868097877 : 160989184] 15.8118949577460
- 1938
1939 [0, 0, 0, 0, 1939]
0
1624199472
{O}
-
1 [-91146 : 385657 : 10648] 9.21628670074096
- 1939
1940 [0, 0, 0, 0, 1940]
0
25404300
{O}
-
1 [157872 : 4874723 : 110592] 10.7301196632173
- 1940
1941 [0, 0, 0, 0, 1941]
0
406887948
{O}
-
1 [-12384330 : -19900493 : 1061208] 12.3146903668302
- 1941
1942 [0, 0, 0, 0, 1942]
0
1629229248
{O}
-
0 - - - 1942
1943 [0, 0, 0, 0, 1943]
0
543635856
{O}
-
1 [-7 : 40 : 1] 3.02110456907200
[-7, 40] 1943
1944 [0, 0, 0, 0, 1944]
0
15552
{O}
-
1 [-2 : 44 : 1] 2.29672767612881
[-2, 44] 1944
1945 [0, 0, 0, 0, 1945]
0
136188900
{O}
-
0 - - - 1945
1946 [0, 0, 0, 0, 1946]
0
1635947712
{O}
-
1 [-51 : 1189 : 27] 5.18706671414495
- 1946
1947 [0, 0, 0, 0, 1947]
0
1637629488
{O}
-
1 [2 : 353 : 8] 4.37313644949286
- 1947
1948 [0, 0, 0, 0, 1948]
0
102457008
{O}
-
1 [66 : 538 : 1] 3.61367552430526
[66, 538] 1948
1949 [0, 0, 0, 0, 1949]
0
410248908
{O}
-
1 [15542340 : 109280951 : 2299968] 12.8085908612063
- 1949
1950 [0, 0, 0, 0, 1950]
0
65707200
{O}
-
1 [-2328228 : -706673141 : 16003008 14.0461718983510
- 1950
1951 [0, 0, 0, 0, 1951]
0
1644365232
{O}
-
2 [66 : 401 : 8],
[757467240 : 5925208343 : 12487168]
4.45842671812803,
15.1264474575684
- 1951
1952 [0, 0, 0, 0, 1952]
0
2143296
{O}
-
1 [-668 : 1827 : 64] 5.27739472107596
- 1952
1953 [0, 0, 0, 0, 1953]
0
45770508
{O}
-
1 [-12 : 15 : 1] 1.87539813262999
[-12, 15] 1953
1954 [0, 0, 0, 0, 1954]
0
549808704
{O}
-
3 [-9 : 35 : 1],
[15 : 73 : 1],
[95 : 927 : 1]
3.04063753395143,
3.25109517787562,
4.08578379404263
[-9, 35], [15, 73], [95, 927] 1954
1955 [0, 0, 0, 0, 1955]
0
1651114800
{O}
-
1 [101 : 1016 : 1] 4.69149339025264
[101, 1016] 1955
1956 [0, 0, 0, 0, 1956]
0
25825068
{O}
-
2 [-8 : 38 : 1],
[-11 : 25 : 1]
2.10763436617469,
3.06028459205170
[-11, 25], [-8, 38], [460, 9866] 1956
1957 [0, 0, 0, 0, 1957]
0
413623692
{O}
-
2 [63 : 502 : 1],
[-5592428877 : -75972917032 : 1732323601]
4.26614764669431,
17.1791519671287
[63, 502] 1957
1958 [0, 0, 0, 0, 1958]
0
1656186048
{O}
-
0 - - - 1958
1959 [0, 0, 0, 0, 1959]
0
1657878192
{O}
-
0 - - - 1959
1960 [0, 0, 0, 0, 1960]
0
2116800
{O}
-
0 - - - 1960
1961 [0, 0, 0, 0, 1961]
0
138438756
{O}
-
2 [4 : 45 : 1],
[-10 : 31 : 1]
1.99602919492101,
2.58913158313553
[-10, 31], [4, 45], [7, 48], [950, 29281] 1961
1962 [0, 0, 0, 0, 1962]
0
184773312
{O}
-
1 [-284 : 2771 : 64] 5.77769448248108
- 1962
1963 [0, 0, 0, 0, 1963]
0
554885136
{O}
-
1 [-3 : 44 : 1] 2.99721320525102
[-3, 44] 1963
1964 [0, 0, 0, 0, 1964]
0
104146992
{O}
-
1 [-17446352 : -239582341 : 5451776] 13.3393291453173
- 1964
1965 [0, 0, 0, 0, 1965]
0
417012300
{O}
-
0 - - - 1965
1966 [0, 0, 0, 0, 1966]
0
1669747392
{O}
-
1 [-9117 : 2303 : 729] 7.47145659159158
- 1966
1967 [0, 0, 0, 0, 1967]
0
1671446448
{O}
-
0 - - - 1967
1968 [0, 0, 0, 0, 1968]
0
6535728
{O}
-
0 - - - 1968
1969 [0, 0, 0, 0, 1969]
0
418711788
{O}
-
1 [-294 : 703 : 27] 4.79627597999907
- 1969
1970 [0, 0, 0, 0, 1970]
0
558849600
{O}
-
1 [10312 : 51557 : 512] 7.56211646176919
- 1970
1971 [0, 0, 0, 0, 1971]
0
767376
{O}
-
0 - - - 1971
1972 [0, 0, 0, 0, 1972]
0
8749764
{O}
-
0 - - - 1972
1973 [0, 0, 0, 0, 1973]
0
420414732
{O}
-
2 [129 : 1232 : 27],
[5418147 : -131053726 : 9261]
5.21495744365052,
12.4739280416964
- 1973
1974 [0, 0, 0, 0, 1974]
0
1683364032
{O}
-
1 [-5 : 43 : 1] 3.01079872595214
[-5, 43] 1974
1975 [0, 0, 0, 0, 1975]
0
67402800
{O}
-
2 [9 : 52 : 1],
[21 : 106 : 1]
3.09186719229834,
3.42816338109394
[9, 52], [21, 106] 1975
1976 [0, 0, 0, 0, 1976]
0
105423552
{O}
-
2 [17 : 83 : 1],
[354 : 1756 : 27]
3.31201837405139,
4.70273287482356
[17, 83] 1976
1977 [0, 0, 0, 0, 1977]
0
422121132
{O}
-
1 [19 : 94 : 1] 3.37072954296684
[19, 94] 1977
1978 [0, 0, 0, 0, 1978]
0
1690193088
{O}
-
0 - - - 1978
1979 [0, 0, 0, 0, 1979]
0
563967504
{O}
-
1 [1261025 : -11349886 : 15625] 10.9246850233604
- 1979
1980 [0, 0, 0, 0, 1980]
0
11761200
{O}
-
2 [-6 : 42 : 1],
[114 : 1218 : 1]
1.59348295812868,
3.37855254445817
[-6, 42], [114, 1218] 1980
1981 [0, 0, 0, 0, 1981]
0
141276996
{O}
-
0 - - - 1981
1982 [0, 0, 0, 0, 1982]
0
1697035968
{O}
-
1 [-6226851 : 22199111 : 658503] 11.9810678091837
- 1982
1983 [0, 0, 0, 0, 1983]
0
1698748848
{O}
-
1 [-9856525119 : -91141373168 : 2102071041] 17.3209690516223
- 1983
1984 [0, 0, 0, 0, 1984]
0
415152
{O}
-
1 [-12 : 16 : 1] 1.68822040963350
[-12, 16] 1984
1985 [0, 0, 0, 0, 1985]
0
425544300
{O}
-
1 [-770 : 5231 : 125] 5.77784938364606
- 1985
1986 [0, 0, 0, 0, 1986]
0
1703892672
{O}
-
2 [626 : 5549 : 8],
[-12776010 : -16475923 : 1061208]
5.84549078065865,
12.3251511114356
- 1986
1987 [0, 0, 0, 0, 1987]
0
1705609008
{O}
-
2 [1245 : 6818 : 125],
[-70380 : -289121 : 8000]
6.33490400997988,
9.03534987303089
- 1987
1988 [0, 0, 0, 0, 1988]
0
8892324
{O}
-
2 [16 : 78 : 1],
[8 : 50 : 1]
1.81012100898465,
2.14795952883168
[8, 50], [16, 78], [232, 3534] 1988
1989 [0, 0, 0, 0, 1989]
0
47473452
{O}
-
0 - - - 1989
1990 [0, 0, 0, 0, 1990]
0
570254400
{O}
-
1 [-1545 : 1261 : 125] 6.29792329031855
- 1990
1991 [0, 0, 0, 0, 1991]
0
1712482992
{O}
-
1 [5 : 46 : 1] 3.02326746953479
[5, 46] 1991
1992 [0, 0, 0, 0, 1992]
0
107137728
{O}
-
1 [14833 : -1806523 : 1] 9.60513141031623
[14833, 1806523] 1992
1993 [0, 0, 0, 0, 1993]
0
428981292
{O}
-
2 [6 : 47 : 1],
[12 : 61 : 1]
2.57522456645954,
2.70752059504918
[6, 47], [12, 61], [306, 5353] 1993
1994 [0, 0, 0, 0, 1994]
0
1717647552
{O}
-
2 [23 : 119 : 1],
[-12000010 : -65811809 : 1643032]
3.48535344106178,
12.5731456892475
[23, 119] 1994
1995 [0, 0, 0, 0, 1995]
0
1719370800
{O}
-
0 - - - 1995
1996 [0, 0, 0, 0, 1996]
0
107568432
{O}
-
0 - - - 1996
1997 [0, 0, 0, 0, 1997]
0
143568324
{O}
-
0 - - - 1997
1998 [0, 0, 0, 0, 1998]
0
2365632
{O}
-
1 [3 : 45 : 1] 1.54039712760551
[3, 45] 1998
1999 [0, 0, 0, 0, 1999]
0
575424144
{O}
-
1 [-977550 : 4874543 : 125000] 10.8610392813483
- 1999
2000 [0, 0, 0, 0, 2000]
0
675
{O}
-
1 [20 : 100 : 1] 0.40559108697430
[-4, 44], [20, 100] 2000

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Last Update: 2021.09.26
H.Nakao

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