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Rational Points on Ellptic Curves: y^2=x^3+n (n \in [5001..6000])


[2021.09.28]y^2=x^3+n (n \in [5001..6000])の有理点



■n=5001,5002,...,6000に対して、
     En: y2 = x3+n
の有理点を求める。

■n=5001,5002,...,6000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=5832
                 =Z/3Z if n=5041,5184,5329,5476,5625,5776,5829
                 ={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(5001,6000)
E_5041(Q)_{tors}=[3, [3], [[0, 71]]]
E_5184(Q)_{tors}=[3, [3], [[0, 72]]]
E_5329(Q)_{tors}=[3, [3], [[0, 73]]]
E_5476(Q)_{tors}=[3, [3], [[0, 74]]]
E_5625(Q)_{tors}=[3, [3], [[0, 75]]]
E_5776(Q)_{tors}=[3, [3], [[0, 76]]]
E_5832(Q)_{tors}=[2, [2], [[-18, 0]]]
E_5929(Q)_{tors}=[3, [3], [[0, 77]]]
time = 6 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
5001 [0, 0, 0, 0, 5001]
0
2701080108
{O}
-
1 [-8 : 67 : 1] 2.86483196959470
[-8, 67] 5001
5002 [0, 0, 0, 0, 5002]
0
10808641728
{O}
-
0 - - - 5002
5003 [0, 0, 0, 0, 5003]
0
3604321296
{O}
-
1 [-46 : 555 : 8] 4.15268778305093
- 5003
5004 [0, 0, 0, 0, 5004]
0
75120048
{O}
-
0 - - - 5004
5005 [0, 0, 0, 0, 5005]
0
901800900
{O}
-
0 - - - 5005
5006 [0, 0, 0, 0, 5006]
0
10825935552
{O}
-
1 [-13 : 53 : 1] 3.35894425679246
[-13, 53] 5006
5007 [0, 0, 0, 0, 5007]
0
10830261168
{O}
-
1 [45563 : 865442 : 12167] 9.58083610023208
- 5007
5008 [0, 0, 0, 0, 5008]
0
2645163
{O}
-
1 [48 : 340 : 1] 2.70867135205358
[48, 340] 5008
5009 [0, 0, 0, 0, 5009]
0
2709728748
{O}
-
1 [56 : 425 : 1] 3.75417217986954
[56, 425] 5009
5010 [0, 0, 0, 0, 5010]
0
10843243200
{O}
-
0 - - - 5010
5011 [0, 0, 0, 0, 5011]
0
10847572272
{O}
-
0 - - - 5011
5012 [0, 0, 0, 0, 5012]
0
56520324
{O}
-
0 - - - 5012
5013 [0, 0, 0, 0, 5013]
0
301562028
{O}
-
2 [-17 : 10 : 1],
[3155 : 18154 : 125]
3.38837763029282,
6.88544728200557
[-17, 10] 5013
5014 [0, 0, 0, 0, 5014]
0
3620188224
{O}
-
1 [3 : 71 : 1] 3.30725980225963
[3, 71] 5014
5015 [0, 0, 0, 0, 5015]
0
10864897200
{O}
-
1 [6805 : 50984 : 125] 7.41259864338024
- 5015
5016 [0, 0, 0, 0, 5016]
0
679326912
{O}
-
1 [-1087484356 : 6813199595 : 107850176] 15.6710460727379
- 5016
5017 [0, 0, 0, 0, 5017]
0
2718391212
{O}
-
0 - - - 5017
5018 [0, 0, 0, 0, 5018]
0
10877899968
{O}
-
0 - - - 5018
5019 [0, 0, 0, 0, 5019]
0
10882235952
{O}
-
0 - - - 5019
5020 [0, 0, 0, 0, 5020]
0
680410800
{O}
-
0 - - - 5020
5021 [0, 0, 0, 0, 5021]
0
907575876
{O}
-
2 [55 : 414 : 1],
[-145 : 8856 : 125]
3.65267258457729,
5.97280900090776
[55, 414] 5021
5022 [0, 0, 0, 0, 5022]
0
14945472
{O}
-
2 [19 : 109 : 1],
[-87 : 1907 : 27]
3.53278369454607,
5.50474682831765
[19, 109] 5022
5023 [0, 0, 0, 0, 5023]
0
3633196176
{O}
-
1 [-55335515641 : 38506108002 : 3261545587] 17.4430418894887
- 5023
5024 [0, 0, 0, 0, 5024]
0
42593472
{O}
-
1 [922761528 : -5523107455 : 30371328] 15.2607987938930
- 5024
5025 [0, 0, 0, 0, 5025]
0
109082700
{O}
-
1 [-5 : 70 : 1] 2.24095987858355
[-5, 70] 5025
5026 [0, 0, 0, 0, 5026]
0
10912612032
{O}
-
1 [-12465 : 3779 : 729] 7.78431946729112
- 5026
5027 [0, 0, 0, 0, 5027]
0
10916954928
{O}
-
0 - - - 5027
5028 [0, 0, 0, 0, 5028]
0
170645292
{O}
-
1 [13 : 85 : 1] 3.41540844585287
[13, 85] 5028
5029 [0, 0, 0, 0, 5029]
0
2731410828
{O}
-
1 [4206255 : 24227312 : 226981] 11.7449433813250
- 5029
5030 [0, 0, 0, 0, 5030]
0
3643329600
{O}
-
1 [98 : 663 : 8] 4.23979928166675
- 5030
5031 [0, 0, 0, 0, 5031]
0
1214926128
{O}
-
0 - - - 5031
5032 [0, 0, 0, 0, 5032]
0
227889216
{O}
-
1 [274 : 1701 : 8] 4.68914912471764
- 5032
5033 [0, 0, 0, 0, 5033]
0
2735757612
{O}
-
2 [2 : 71 : 1],
[-470 : 8821 : 125]
2.84348285716539,
6.06667072765714
[2, 71] 5033
5034 [0, 0, 0, 0, 5034]
0
10947379392
{O}
-
1 [-17 : 11 : 1] 3.38959385121918
[-17, 11] 5034
5035 [0, 0, 0, 0, 5035]
0
10951729200
{O}
-
1 [4049640 : -32531789 : 64000] 11.6940125265738
- 5035
5036 [0, 0, 0, 0, 5036]
0
684754992
{O}
-
0 - - - 5036
5037 [0, 0, 0, 0, 5037]
0
2740107852
{O}
-
1 [-527130459661650480593912595367335 : 5977524328502113607018431732672418 : 86203243842042074097880987545375] 52.3424091382705
- 5037
5038 [0, 0, 0, 0, 5038]
0
10964783808
{O}
-
0 - - - 5038
5039 [0, 0, 0, 0, 5039]
0
3656379024
{O}
-
1 [6475 : 37206 : 343] 6.87339059055780
- 5039
5040 [0, 0, 0, 0, 5040]
0
4762800
{O}
-
1 [1 : 71 : 1] 3.30435813006641
[1, 71] 5040
5041 [0, 0, 0, 0, 5041]
0
181476
Z/3Z
[0, 71]
1 [30 : 179 : 1] 3.30528823880071
[0, 71], [30, 179] 5041
5042 [0, 0, 0, 0, 5042]
0
10982202048
{O}
-
3 [-1 : 71 : 1],
[514 : 4159 : 8],
[26246 : 757205 : 10648]
3.30445723028249,
5.71529229750218,
9.48945763347173
[-1, 71] 5042
5043 [0, 0, 0, 0, 5043]
0
6535728
{O}
-
2 [37 : 236 : 1],
[241 : 3742 : 1]
3.90489751415123,
5.52860517550447
[37, 236], [241, 3742] 5043
5044 [0, 0, 0, 0, 5044]
0
171733068
{O}
-
0 - - - 5044
5045 [0, 0, 0, 0, 5045]
0
2748818700
{O}
-
1 [771122948708 : 12394897272043 : 172994909248] 20.5669623146937
- 5045
5046 [0, 0, 0, 0, 5046]
0
13079232
{O}
-
1 [67 : 553 : 1] 4.36398691179665
[67, 553] 5046
5047 [0, 0, 0, 0, 5047]
0
224571312
{O}
-
2 [9 : 76 : 1],
[245196369 : 2006650864 : 26198073]
3.35665201586575,
14.7486251691100
[9, 76] 5047
5048 [0, 0, 0, 0, 5048]
0
229340736
{O}
-
1 [-14 : 48 : 1] 2.12604347793681
[-14, 48] 5048
5049 [0, 0, 0, 0, 5049]
0
3776652
{O}
-
1 [-2 : 71 : 1] 2.84427358454023
[-2, 71] 5049
5050 [0, 0, 0, 0, 5050]
0
146894400
{O}
-
0 - - - 5050
5051 [0, 0, 0, 0, 5051]
0
11021443632
{O}
-
1 [-24141309970105222881902440 : -479503886853297624678996137 : 6777277781588374372300288] 41.4275177230745
- 5051
5052 [0, 0, 0, 0, 5052]
0
689113008
{O}
-
1 [-11 : 61 : 1] 3.34827869948731
[-11, 61] 5052
5053 [0, 0, 0, 0, 5053]
0
2757543372
{O}
-
2 [-51 : 1918 : 27],
[4860054 : -29228633 : 157464]
5.50365424173952,
11.7632984435205
- 5053
5054 [0, 0, 0, 0, 5054]
0
30566592
{O}
-
0 - - - 5054
5055 [0, 0, 0, 0, 5055]
0
11038906800
{O}
-
0 - - - 5055
5056 [0, 0, 0, 0, 5056]
0
2696112
{O}
-
2 [-15 : 41 : 1],
[180 : 2416 : 1]
3.37614418975677,
3.86541416561391
[-15, 41], [180, 2416] 5056
5057 [0, 0, 0, 0, 5057]
0
920636964
{O}
-
2 [-17 : 12 : 1],
[-16 : 31 : 1]
2.84161428910284,
2.92140864126034
[-17, 12], [-16, 31], [394, 7821], [1882, 81645] 5057
5058 [0, 0, 0, 0, 5058]
0
1228001472
{O}
-
0 - - - 5058
5059 [0, 0, 0, 0, 5059]
0
3685461264
{O}
-
1 [5 : 72 : 1] 2.77077199465867
[5, 72] 5059
5060 [0, 0, 0, 0, 5060]
0
172824300
{O}
-
0 - - - 5060
5061 [0, 0, 0, 0, 5061]
0
2766281868
{O}
-
0 - - - 5061
5062 [0, 0, 0, 0, 5062]
0
11069500608
{O}
-
1 [32601 : -1132831 : 27] 9.30223206225875
- 5062
5063 [0, 0, 0, 0, 5063]
0
11073874608
{O}
-
2 [41 : 272 : 1],
[24531733012 : 3075426559451 : 1560896]
3.97807334218224,
19.1703151013426
[41, 272] 5063
5064 [0, 0, 0, 0, 5064]
0
692390592
{O}
-
2 [46 : 320 : 1],
[-10818 : 30896 : 729]
3.37022991949698,
7.07675611080279
[46, 320] 5064
5065 [0, 0, 0, 0, 5065]
0
2770656300
{O}
-
1 [1848 : 15409 : 27] 6.11721315390282
- 5065
5066 [0, 0, 0, 0, 5066]
0
3695667264
{O}
-
1 [-5383 : 11885 : 343] 7.27360311736321
- 5066
5067 [0, 0, 0, 0, 5067]
0
1232375472
{O}
-
1 [730869938479587 : 4175100355031018 : 31372112043819] 24.3444771105859
- 5067
5068 [0, 0, 0, 0, 5068]
0
231161616
{O}
-
1 [-3 : 71 : 1] 3.30991685526235
[-3, 71] 5068
5069 [0, 0, 0, 0, 5069]
0
2775034188
{O}
-
2 [11 : 80 : 1],
[605808494 : -8814277223 : 2863288]
3.38521534966519,
15.3162485530297
[11, 80] 5069
5070 [0, 0, 0, 0, 5070]
0
65707200
{O}
-
1 [91 : 871 : 1] 2.91778174157533
[91, 871] 5070
5071 [0, 0, 0, 0, 5071]
0
11108897712
{O}
-
1 [-78 : 515 : 8] 4.72785319089771
- 5071
5072 [0, 0, 0, 0, 5072]
0
2713203
{O}
-
0 - - - 5072
5073 [0, 0, 0, 0, 5073]
0
2779415532
{O}
-
1 [10323 : 64846 : 729] 7.83282136446511
- 5073
5074 [0, 0, 0, 0, 5074]
0
11122045632
{O}
-
0 - - - 5074
5075 [0, 0, 0, 0, 5075]
0
148352400
{O}
-
0 - - - 5075
5076 [0, 0, 0, 0, 5076]
0
79524
{O}
-
1 [-30 : 567 : 8] 3.05103774357938
- 5076
5077 [0, 0, 0, 0, 5077]
0
927933444
{O}
-
2 [47 : 330 : 1],
[1918 : 195525 : 2744]
3.53061249947445,
8.03532514532900
[47, 330] 5077
5078 [0, 0, 0, 0, 5078]
0
11139588288
{O}
-
1 [9665056 : 166006297 : 32768] 12.6541567348132
- 5078
5079 [0, 0, 0, 0, 5079]
0
11143976112
{O}
-
1 [2212 : 13781 : 64] 6.63184277589309
- 5079
5080 [0, 0, 0, 0, 5080]
0
696772800
{O}
-
1 [-10911939 : -64276319 : 1030301] 12.5776062136648
- 5080
5081 [0, 0, 0, 0, 5081]
0
2788188588
{O}
-
1 [118915 : 681842 : 4913] 9.31289211644720
- 5081
5082 [0, 0, 0, 0, 5082]
0
92207808
{O}
-
1 [-17 : 13 : 1] 3.39235594190198
[-17, 13] 5082
5083 [0, 0, 0, 0, 5083]
0
11161536048
{O}
-
2 [18 : 571 : 8],
[-24126192 : -201537829 : 2985984]
4.69576289070077,
13.2721786536120
- 5083
5084 [0, 0, 0, 0, 5084]
0
232623504
{O}
-
1 [10 : 78 : 1] 2.12929834324688
[10, 78] 5084
5085 [0, 0, 0, 0, 5085]
0
310286700
{O}
-
1 [-9 : 66 : 1] 2.60551848291546
[-9, 66] 5085
5086 [0, 0, 0, 0, 5086]
0
3724905024
{O}
-
1 [35 : 219 : 1] 3.31853603791779
[35, 219] 5086
5087 [0, 0, 0, 0, 5087]
0
11179109808
{O}
-
1 [17 : 100 : 1] 3.49402476801732
[17, 100] 5087
5088 [0, 0, 0, 0, 5088]
0
43685568
{O}
-
1 [589701 : 4751783 : 9261] 10.4111172052343
- 5088
5089 [0, 0, 0, 0, 5089]
0
2796975468
{O}
-
2 [15 : 92 : 1],
[123 : 1366 : 1]
3.45480777321667,
4.89852095395637
[15, 92], [123, 1366] 5089
5090 [0, 0, 0, 0, 5090]
0
11192299200
{O}
-
0 - - - 5090
5091 [0, 0, 0, 0, 5091]
0
11196697392
{O}
-
2 [97 : 958 : 1],
[55505 : 397102 : 4913]
4.68443981628169,
9.05734343797651
[97, 958] 5091
5092 [0, 0, 0, 0, 5092]
0
175017132
{O}
-
1 [-12 : 58 : 1] 2.43310933391651
[-12, 58] 5092
5093 [0, 0, 0, 0, 5093]
0
933791364
{O}
-
0 - - - 5093
5094 [0, 0, 0, 0, 5094]
0
1245544128
{O}
-
1 [20062702 : 115051501 : 830584] 12.7324095875346
- 5094
5095 [0, 0, 0, 0, 5095]
0
3738099600
{O}
-
1 [6005731996806 : 35030166388217 : 221884645464] 21.1247555336487
- 5095
5096 [0, 0, 0, 0, 5096]
0
14309568
{O}
-
1 [-10 : 64 : 1] 2.65148991249340
[-10, 64] 5096
5097 [0, 0, 0, 0, 5097]
0
2805776172
{O}
-
0 - - - 5097
5098 [0, 0, 0, 0, 5098]
0
11227508928
{O}
-
1 [-32574820026 : -95782668155 : 2207155608] 17.7201790819892
- 5098
5099 [0, 0, 0, 0, 5099]
0
11231914032
{O}
-
2 [-3450 : 6913 : 216],
[-44985 : 176374 : 3375]
6.96925472815098,
8.78290682942181
- 5099
5100 [0, 0, 0, 0, 5100]
0
28090800
{O}
-
1 [70 : 590 : 1] 2.63527561218243
[70, 590] 5100
5101 [0, 0, 0, 0, 5101]
0
2810181708
{O}
-
1 [-8943 : 92192 : 1331] 8.12234053372634
- 5101
5102 [0, 0, 0, 0, 5102]
0
3748378176
{O}
-
1 [20308643 : 120071385 : 704969] 12.1723478984358
- 5102
5103 [0, 0, 0, 0, 5103]
0
21168
{O}
-
0 - - - 5103
5104 [0, 0, 0, 0, 5104]
0
14653584
{O}
-
1 [-7 : 69 : 1] 2.77883804102640
[-7, 69] 5104
5105 [0, 0, 0, 0, 5105]
0
2814590700
{O}
-
2 [-4 : 71 : 1],
[104 : 1063 : 1]
2.85326632484512,
4.28465600062320
[-4, 71], [104, 1063] 5105
5106 [0, 0, 0, 0, 5106]
0
11262773952
{O}
-
1 [127 : 1433 : 1] 4.92787917317875
[127, 1433] 5106
5107 [0, 0, 0, 0, 5107]
0
11267185968
{O}
-
1 [15246 : 199361 : 2744] 8.60497474528422
- 5107
5108 [0, 0, 0, 0, 5108]
0
176118732
{O}
-
1 [26503195 : 159587129 : 857375] 12.8953957515904
- 5108
5109 [0, 0, 0, 0, 5109]
0
2819003148
{O}
-
1 [-17 : 14 : 1] 3.39389884039509
[-17, 14] 5109
5110 [0, 0, 0, 0, 5110]
0
11280427200
{O}
-
2 [-444 : 4423 : 64],
[12246 : 93491 : 216]
6.10079524996696,
7.81100525422756
- 5110
5111 [0, 0, 0, 0, 5111]
0
3761614224
{O}
-
1 [25 : 144 : 1] 3.11511851825073
[25, 144] 5111
5112 [0, 0, 0, 0, 5112]
0
78397632
{O}
-
0 - - - 5112
5113 [0, 0, 0, 0, 5113]
0
941139684
{O}
-
2 [-13 : 54 : 1],
[6 : 73 : 1]
2.81605328656007,
2.86844052131614
[-13, 54], [6, 73], [8, 75], [5462, 403671] 5113
5114 [0, 0, 0, 0, 5114]
0
11298094272
{O}
-
1 [290050668258073501835392129668 : -8838561821859887291819663724665 : 312364145036564877656812608] 47.5158611871514
- 5114
5115 [0, 0, 0, 0, 5115]
0
11302513200
{O}
-
1 [1418313284598977 : -20007145577744876 : 276110645956613] 25.4923889161488
- 5115
5116 [0, 0, 0, 0, 5116]
0
706683312
{O}
-
1 [-6 : 70 : 1] 2.63093251287896
[-6, 70] 5116
5117 [0, 0, 0, 0, 5117]
0
2827838412
{O}
-
1 [-10390 : 63209 : 1000] 7.95352267933502
- 5117
5118 [0, 0, 0, 0, 5118]
0
11315775168
{O}
-
2 [-94 : 473 : 8],
[-159137 : -3612731 : 50653]
4.74349693820060,
10.5353854733951
- 5118
5119 [0, 0, 0, 0, 5119]
0
11320197552
{O}
-
0 - - - 5119
5120 [0, 0, 0, 0, 5120]
0
225
{O}
-
1 [9 : 77 : 1] 3.36551678303670
[9, 77] 5120
5121 [0, 0, 0, 0, 5121]
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1 [148647802345 : -1356748091908 : 16679103875] 19.0943534596244
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0
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2 [19 : 113 : 1],
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3.56600430209720,
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[19, 113] 5910
5911 [0, 0, 0, 0, 5911]
0
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0 - - - 5911
5912 [0, 0, 0, 0, 5912]
0
314565696
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1 [224315 : 3336327 : 42875] 9.93319796395684
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2 [-18 : 9 : 1],
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1.51677277850845,
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[-18, 9], [-9, 72], [76, 667], [108, 1125], [2952, 160389] 5913
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1 [-264342 : -880901 : 17576] 9.93936684958665
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5915 [0, 0, 0, 0, 5915]
0
89434800
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1 [1014 : 16757 : 216] 5.24249688355364
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5916 [0, 0, 0, 0, 5916]
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944974512
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1 [-4662 : 54818 : 729] 7.07423698571114
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2 [27 : 160 : 1],
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2 [-13 : 61 : 1],
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14.8064323641742
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2 [-5460 : 132589 : 1728],
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8.33147163383141,
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0 - - - 5920
5921 [0, 0, 0, 0, 5921]
0
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2 [2 : 77 : 1],
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[2, 77] 5921
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0 - - - 5922
5923 [0, 0, 0, 0, 5923]
0
5051797776
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1 [-62 : 591 : 8] 4.21666864151407
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2 [20 : 118 : 1],
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1 [-625053 : 925552 : 35937] 10.4330072406066
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5926 [0, 0, 0, 0, 5926]
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1 [3697758813 : 23057138113 : 109902239] 16.2028469693408
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3.35839562805301,
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[0, 77]
0 - - - 5929
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3 [31 : 189 : 1],
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3.25917356663097,
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6.78689183352030
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1 [2872031799 : 17320430474 : 160103007] 16.1402995348022
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1 [-18 : 10 : 1] 2.75147308674390
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0 - - - 5933
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1 [-22986827482458978705 : -322619644987324556507 : 4245271877139040125] 31.9647371271542
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1 [126152802194293261289790432055811058418334127 : 1974987300231056859483952352026842712389608546 : 514917121744965888025994865652851225188683] 69.5766277212473
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0 - - - 5936
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3 [-2 : 77 : 1],
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2.89808379610908,
3.43782932063380,
6.13807709170959
[-17, 32], [-2, 77], [724, 19481] 5937
5938 [0, 0, 0, 0, 5938]
0
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2 [5064 : 42547 : 512],
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7.57435923539898,
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1 [194 : 1137 : 8] 4.51004296104489
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0 - - - 5940
5941 [0, 0, 0, 0, 5941]
0
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0 - - - 5941
5942 [0, 0, 0, 0, 5942]
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1 [15512025753726697 : 521434752965905247 : 6757593590932379] 27.6609651622957
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1 [583087273 : -14738310124 : 912673] 15.6265764702099
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0
953940672
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1 [-429 : 1187 : 27] 5.62770003772224
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0
3817046700
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1 [-16 : 43 : 1] 2.96919115532190
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5946 [0, 0, 0, 0, 5946]
0
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0 - - - 5946
5947 [0, 0, 0, 0, 5947]
0
15278461488
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0 - - - 5947
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0
318408336
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1 [9305 : 80859 : 125] 7.13086399755804
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1 [1374726 : -8078343 : 54872] 10.2324867083979
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1 [26722470 : 157109617 : 1061208] 12.9423281120112
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2 [-29652 : 51875 : 1728],
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8.40959899542389,
17.9860296593155
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2 [-11 : 68 : 1],
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3.39933306484954,
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1 [-3 : 77 : 1] 3.36332081518650
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1 [2721 : 27395 : 27] 6.92145985206287
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1 [5 : 78 : 1] 2.82371393202978
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1 [-62 : 593 : 8] 4.76797065157914
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1 [50832 : 363445 : 4096] 8.99615537598104
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1 [-2226 : 211919 : 2744] 8.63840107594291
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1 [35 : 221 : 1] 3.88575150689019
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1 [-7 : 75 : 1] 2.82919588737069
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1 [155331133413 : 2432955505463 : 31166657523] 19.4819364957242
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1 [-12445909725467547307839 : -69470322674549741425720 : 1055376763381269992187] 35.6772166049187
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1 [-123 : 2071 : 27] 5.56633722412241
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1 [870 : 16793 : 216] 6.95274522918271
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1 [6512226 : -217001494 : 2803221] 12.5678879503403
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1 [-53083978 : -304049603 : 4574296] 13.6283269143090
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2 [34 : 569 : 8],
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1 [25 : 147 : 1] 3.14028947457971
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1 [17610 : 106991 : 1000] 8.14699380013194
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1 [3202 : 64063 : 8] 7.40629729035570
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2 [-8 : 74 : 1],
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2 [-6 : 76 : 1],
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2 [-14 : 57 : 1],
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2 [223 : 3331 : 1],
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1 [9 : 82 : 1] 3.40804226778608
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1 [184528831725 : 1081724857757 : 8303765625] 18.8600880477717
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1 [904499082604407 : -16123529893677451 : 2846986195717] 24.9145047674335
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0 - - - 6000

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Last Update: 2021.09.28
H.Nakao

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