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Rational Points on Ellptic Curves: y^2=x^3+n (n \in [3001..4000])


[2021.08.31]y^2=x^3+n (n \in [3001..4000])の有理点



■n=3001,3002,...,4000に対して、
     En: y2 = x3+n
の有理点を求める。

■n=3001,3002,...,4000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=3375
                 =Z/3Z if n=3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969
                 ={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(3001,4000)
E_3025(Q)_{tors}=[3, [3], [[0, 55]]]
E_3136(Q)_{tors}=[3, [3], [[0, 56]]]
E_3249(Q)_{tors}=[3, [3], [[0, 57]]]
E_3364(Q)_{tors}=[3, [3], [[0, 58]]]
E_3375(Q)_{tors}=[2, [2], [[-15, 0]]]
E_3481(Q)_{tors}=[3, [3], [[0, 59]]]
E_3600(Q)_{tors}=[3, [3], [[0, 60]]]
E_3721(Q)_{tors}=[3, [3], [[0, 61]]]
E_3844(Q)_{tors}=[3, [3], [[0, 62]]]
E_3969(Q)_{tors}=[3, [3], [[0, 63]]]
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
3001 [0, 0, 0, 0, 3001]
0
972648108
{O}
-
0 - - - 3001
3002 [0, 0, 0, 0, 3002]
0
3893185728
{O}
-
0 - - - 3002
3003 [0, 0, 0, 0, 3003]
0
3895779888
{O}
-
0 - - - 3003
3004 [0, 0, 0, 0, 3004]
0
243648432
{O}
-
2 [18 : 94 : 1],
[-24180 : 28081 : 1728]
2.71886013635103,
8.18448856662778
[18, 94] 3004
3005 [0, 0, 0, 0, 3005]
0
325080900
{O}
-
0 - - - 3005
3006 [0, 0, 0, 0, 3006]
0
433729728
{O}
-
0 - - - 3006
3007 [0, 0, 0, 0, 3007]
0
1302055056
{O}
-
1 [-357 : 712 : 27] 5.40542532928843
- 3007
3008 [0, 0, 0, 0, 3008]
0
954288
{O}
-
1 [17 : 89 : 1] 3.38676609979565
[17, 89] 3008
3009 [0, 0, 0, 0, 3009]
0
977840748
{O}
-
0 - - - 3009
3010 [0, 0, 0, 0, 3010]
0
3913963200
{O}
-
1 [-201987 : 864557 : 19683] 9.77526617595028
- 3010
3011 [0, 0, 0, 0, 3011]
0
3916564272
{O}
-
2 [5 : 56 : 1],
[-22240522 : -37851905 : 1643032]
3.15376453240038,
12.7527063267667
[5, 56] 3011
3012 [0, 0, 0, 0, 3012]
0
61236972
{O}
-
3 [-8 : 50 : 1],
[-11 : 41 : 1],
[292 : 4990 : 1]
2.24230004562096,
3.18980740318648,
4.78299074258534
[-11, 41], [-8, 50], [28, 158], [292, 4990] 3012
3013 [0, 0, 0, 0, 3013]
0
980442252
{O}
-
1 [-5304 : 22325 : 512] 7.34356438912723
- 3013
3014 [0, 0, 0, 0, 3014]
0
1308124224
{O}
-
1 [100065 : -6091741 : 27] 10.4173600673556
- 3014
3015 [0, 0, 0, 0, 3015]
0
436330800
{O}
-
1 [264206476 : 6481832471 : 438976] 15.0762720616734
- 3015
3016 [0, 0, 0, 0, 3016]
0
81866304
{O}
-
1 [-470 : 6804 : 125] 5.11806443382922
- 3016
3017 [0, 0, 0, 0, 3017]
0
983047212
{O}
-
2 [2 : 55 : 1],
[55 : 6866 : 125]
2.67383715137237,
6.35179161003538
[2, 55] 3017
3018 [0, 0, 0, 0, 3018]
0
3934795968
{O}
-
1 [146 : 763 : 8] 4.80552420280383
- 3018
3019 [0, 0, 0, 0, 3019]
0
3937403952
{O}
-
1 [-1755 : 1982 : 125] 6.43542046364587
- 3019
3020 [0, 0, 0, 0, 3020]
0
246250800
{O}
-
0 - - - 3020
3021 [0, 0, 0, 0, 3021]
0
985655628
{O}
-
1 [7 : 58 : 1] 3.17740127034388
[7, 58] 3021
3022 [0, 0, 0, 0, 3022]
0
3945233088
{O}
-
0 - - - 3022
3023 [0, 0, 0, 0, 3023]
0
1315948176
{O}
-
1 [-22361354 : -36816255 : 1643032] 12.2052126675229
- 3023
3024 [0, 0, 0, 0, 3024]
0
1323
{O}
-
1 [-12 : 36 : 1] 0.34825623556644
[-12, 36], [1, 55], [60, 468] 3024
3025 [0, 0, 0, 0, 3025]
0
108900
Z/3Z
[0, 55]
2 [-10 : 45 : 1],
[-6 : 53 : 1]
1.09865803802053,
2.69240358979704
[-10, 45], [-6, 53], [0, 55], [11, 66], [15, 80], [20, 105], [44, 297], [66, 539], [110, 1155], [330, 5995], [1334, 48723] 3025
3026 [0, 0, 0, 0, 3026]
0
3955684032
{O}
-
1 [-1 : 55 : 1] 3.13447120685281
[-1, 55] 3026
3027 [0, 0, 0, 0, 3027]
0
3958298928
{O}
-
1 [626 : 5555 : 8] 5.86063653083811
- 3027
3028 [0, 0, 0, 0, 3028]
0
61889292
{O}
-
0 - - - 3028
3029 [0, 0, 0, 0, 3029]
0
990882828
{O}
-
1 [13366433 : -90631280 : 300763] 12.4073674558610
- 3029
3030 [0, 0, 0, 0, 3030]
0
3966148800
{O}
-
0 - - - 3030
3031 [0, 0, 0, 0, 3031]
0
3968767152
{O}
-
0 - - - 3031
3032 [0, 0, 0, 0, 3032]
0
82737216
{O}
-
1 [14 : 76 : 1] 2.62104859517548
[14, 76] 3032
3033 [0, 0, 0, 0, 3033]
0
110389068
{O}
-
3 [-9 : 48 : 1],
[-2 : 55 : 1],
[-14 : 17 : 1]
2.44365718468115,
2.67515298779479,
2.75544552912716
[-14, 17], [-9, 48], [-2, 55], [6, 57], [12, 69], [52, 379], [192, 2661], [423, 8700] 3033
3034 [0, 0, 0, 0, 3034]
0
1325542464
{O}
-
1 [215 : 3153 : 1] 4.86278242858593
[215, 3153] 3034
3035 [0, 0, 0, 0, 3035]
0
3979249200
{O}
-
1 [253829060121304247900572812 : -30976340372771009884474709323 : 17043697200902927631552] 43.7359453768620
- 3035
3036 [0, 0, 0, 0, 3036]
0
248866992
{O}
-
1 [32330 : -519986 : 125] 8.11562018771582
- 3036
3037 [0, 0, 0, 0, 3037]
0
996123852
{O}
-
0 - - - 3037
3038 [0, 0, 0, 0, 3038]
0
81369792
{O}
-
2 [-13 : 29 : 1],
[-41021 : 243475 : 4913]
3.20930131803005,
8.83815512360751
[-13, 29] 3038
3039 [0, 0, 0, 0, 3039]
0
3989745072
{O}
-
2 [-46 : 427 : 8],
[-25420 : 438683 : 8000]
4.54077639808834,
9.13319302029933
- 3039
3040 [0, 0, 0, 0, 3040]
0
15595200
{O}
-
0 - - - 3040
3041 [0, 0, 0, 0, 3041]
0
332916516
{O}
-
2 [-5 : 54 : 1],
[22 : 117 : 1]
2.60113508795495,
2.50455933387943
[-5, 54], [22, 117] 3041
3042 [0, 0, 0, 0, 3042]
0
2628288
{O}
-
1 [67998721 : -634391711 : 11089567] 13.9830523187905
- 3042
3043 [0, 0, 0, 0, 3043]
0
1333418256
{O}
-
1 [-3503497 : 11501436 : 300763] 11.0583685674619
- 3043
3044 [0, 0, 0, 0, 3044]
0
62545068
{O}
-
0 - - - 3044
3045 [0, 0, 0, 0, 3045]
0
1001378700
{O}
-
0 - - - 3045
3046 [0, 0, 0, 0, 3046]
0
4008146112
{O}
-
1 [210 : 1163 : 8] 5.00716148239080
- 3046
3047 [0, 0, 0, 0, 3047]
0
4010778288
{O}
-
2 [-7 : 52 : 1],
[147882889 : 2661707126 : 456533]
3.16320933061910,
14.4956628425159
[-7, 52] 3047
3048 [0, 0, 0, 0, 3048]
0
250838208
{O}
-
0 - - - 3048
3049 [0, 0, 0, 0, 3049]
0
1004011308
{O}
-
1 [108192 : -745285 : 12167] 9.01783125320450
- 3049
3050 [0, 0, 0, 0, 3050]
0
53582400
{O}
-
0 - - - 3050
3051 [0, 0, 0, 0, 3051]
0
5516208
{O}
-
0 - - - 3051
3052 [0, 0, 0, 0, 3052]
0
83832336
{O}
-
1 [-3 : 55 : 1] 3.14246748880000
[-3, 55] 3052
3053 [0, 0, 0, 0, 3053]
0
1006647372
{O}
-
0 - - - 3053
3054 [0, 0, 0, 0, 3054]
0
4029227712
{O}
-
1 [-10283557242 : 166005898201 : 3023464536] 17.6973456799794
- 3054
3055 [0, 0, 0, 0, 3055]
0
4031866800
{O}
-
1 [18 : 443 : 8] 4.52724133758028
- 3055
3056 [0, 0, 0, 0, 3056]
0
15759792
{O}
-
0 - - - 3056
3057 [0, 0, 0, 0, 3057]
0
1009286892
{O}
-
1 [118 : 1283 : 1] 4.38445794144769
[118, 1283] 3057
3058 [0, 0, 0, 0, 3058]
0
4039789248
{O}
-
0 - - - 3058
3059 [0, 0, 0, 0, 3059]
0
1347477264
{O}
-
1 [60995 : -419418 : 1331] 8.26948285201619
- 3059
3060 [0, 0, 0, 0, 3060]
0
7022700
{O}
-
1 [21 : 111 : 1] 2.75923304427379
[21, 111] 3060
3061 [0, 0, 0, 0, 3061]
0
337309956
{O}
-
0 - - - 3061
3062 [0, 0, 0, 0, 3062]
0
4050364608
{O}
-
1 [-6016533 : -449326385 : 8120601] 13.7447049993139
- 3062
3063 [0, 0, 0, 0, 3063]
0
4053010608
{O}
-
1 [31171 : -297758 : 343] 8.50010315510484
- 3063
3064 [0, 0, 0, 0, 3064]
0
253478592
{O}
-
1 [-30 : 439 : 8] 4.53306891894871
- 3064
3065 [0, 0, 0, 0, 3065]
0
1014576300
{O}
-
1 [332488 : -1864051 : 12167] 9.45611145465082
- 3065
3066 [0, 0, 0, 0, 3066]
0
4060953792
{O}
-
0 - - - 3066
3067 [0, 0, 0, 0, 3067]
0
4063603248
{O}
-
2 [579 : 3070 : 27],
[4905 : 31496 : 125]
5.70045820954060,
7.12132183084952
- 3067
3068 [0, 0, 0, 0, 3068]
0
84713616
{O}
-
1 [-14 : 18 : 1] 1.97844458429597
[-14, 18] 3068
3069 [0, 0, 0, 0, 3069]
0
113025132
{O}
-
0 - - - 3069
3070 [0, 0, 0, 0, 3070]
0
1357185600
{O}
-
1 [-3297721 : -411483 : 226981] 10.8981795359329
- 3070
3071 [0, 0, 0, 0, 3071]
0
4074209712
{O}
-
1 [14442545440518 : -87760631606993 : 420863309784] 21.6469706275174
- 3071
3072 [0, 0, 0, 0, 3072]
0
3888
{O}
-
1 [4 : 56 : 1] 1.76580333576025
[4, 56] 3072
3073 [0, 0, 0, 0, 3073]
0
1019879532
{O}
-
2 [36 : 223 : 1],
[-636 : 2927 : 64]
3.37610267828625,
5.95994978922772
[36, 223] 3073
3074 [0, 0, 0, 0, 3074]
0
4082173632
{O}
-
0 - - - 3074
3075 [0, 0, 0, 0, 3075]
0
163393200
{O}
-
1 [-357 : 746 : 27] 5.41202406534384
- 3075
3076 [0, 0, 0, 0, 3076]
0
63866988
{O}
-
1 [24 : 130 : 1] 2.64324491605205
[24, 130] 3076
3077 [0, 0, 0, 0, 3077]
0
340845444
{O}
-
0 - - - 3077
3078 [0, 0, 0, 0, 3078]
0
5614272
{O}
-
0 - - - 3078
3079 [0, 0, 0, 0, 3079]
0
1365154704
{O}
-
1 [31566179 : 323816052 : 300763] 12.5991704951645
- 3079
3080 [0, 0, 0, 0, 3080]
0
256132800
{O}
-
1 [6249818 : -69479108 : 50653] 11.4167225665659
- 3080
3081 [0, 0, 0, 0, 3081]
0
1025196588
{O}
-
2 [40 : 259 : 1],
[64 : 515 : 1]
3.45531472711293,
3.83794375804104
[40, 259], [64, 515] 3081
3082 [0, 0, 0, 0, 3082]
0
4103448768
{O}
-
1 [-29069586 : -7242299 : 2000376] 12.8994658056349
- 3082
3083 [0, 0, 0, 0, 3083]
0
4106112048
{O}
-
0 - - - 3083
3084 [0, 0, 0, 0, 3084]
0
256798512
{O}
-
0 - - - 3084
3085 [0, 0, 0, 0, 3085]
0
1027860300
{O}
-
1 [441699 : 2316974 : 24389] 10.1542066829956
- 3085
3086 [0, 0, 0, 0, 3086]
0
1371369024
{O}
-
1 [-905 : 6503 : 125] 6.38773134383893
- 3086
3087 [0, 0, 0, 0, 3087]
0
190512
{O}
-
0 - - - 3087
3088 [0, 0, 0, 0, 3088]
0
335241
{O}
-
1 [8 : 60 : 1] 1.26262707359344
[8, 60] 3088
3089 [0, 0, 0, 0, 3089]
0
1030527468
{O}
-
2 [-4 : 55 : 1],
[146 : 1765 : 1]
2.68845426205264,
4.58298130360373
[-4, 55], [146, 1765] 3089
3090 [0, 0, 0, 0, 3090]
0
4124779200
{O}
-
1 [237 : 1657 : 27] 5.40802843419514
- 3090
3091 [0, 0, 0, 0, 3091]
0
4127449392
{O}
-
1 [-28759859102306687077086 : -139912244041643002254071 : 2985149246439227906312] 36.1520836415501
- 3091
3092 [0, 0, 0, 0, 3092]
0
64533132
{O}
-
1 [-1541 : 676555 : 12167] 9.41195592164817
- 3092
3093 [0, 0, 0, 0, 3093]
0
1033198092
{O}
-
1 [12581778 : -84755125 : 287496] 12.3666557228182
- 3093
3094 [0, 0, 0, 0, 3094]
0
4135465152
{O}
-
2 [834 : 8527 : 8],
[3653040 : -21877829 : 110592]
6.11938111387257,
11.5190760697431
- 3094
3095 [0, 0, 0, 0, 3095]
0
1379379600
{O}
-
1 [-11 : 42 : 1] 2.64874545571264
[-11, 42] 3095
3096 [0, 0, 0, 0, 3096]
0
28755648
{O}
-
1 [10 : 64 : 1] 2.53986731078376
[10, 64] 3096
3097 [0, 0, 0, 0, 3097]
0
345290724
{O}
-
2 [-13 : 30 : 1],
[-12 : 37 : 1]
2.66568912833457,
2.74441617439418
[-13, 30], [-12, 37], [74, 639], [4514, 303279] 3097
3098 [0, 0, 0, 0, 3098]
0
4146164928
{O}
-
1 [-245 : 6949 : 125] 6.36305634985552
- 3098
3099 [0, 0, 0, 0, 3099]
0
4148842032
{O}
-
1 [-36865734 : 48366253 : 2628072] 13.0785877476303
- 3099
3100 [0, 0, 0, 0, 3100]
0
10378800
{O}
-
0 - - - 3100
3101 [0, 0, 0, 0, 3101]
0
1038549708
{O}
-
1 [104949820270 : 723263028851 : 11697083000] 18.6701529967545
- 3101
3102 [0, 0, 0, 0, 3102]
0
4156878528
{O}
-
0 - - - 3102
3103 [0, 0, 0, 0, 3103]
0
4159559088
{O}
-
0 - - - 3103
3104 [0, 0, 0, 0, 3104]
0
5419584
{O}
-
1 [65 : 527 : 1] 4.31368881570261
[65, 527] 3104
3105 [0, 0, 0, 0, 3105]
0
1428300
{O}
-
1 [-14 : 19 : 1] 2.76230670371432
[-14, 19] 3105
3106 [0, 0, 0, 0, 3106]
0
1389201984
{O}
-
1 [47 : 327 : 1] 3.49490527153093
[47, 327] 3106
3107 [0, 0, 0, 0, 3107]
0
4170289968
{O}
-
1 [479432645792372 : 2816665109977285 : 41120783500096] 24.1654753628518
- 3107
3108 [0, 0, 0, 0, 3108]
0
65202732
{O}
-
0 - - - 3108
3109 [0, 0, 0, 0, 3109]
0
1043915148
{O}
-
2 [3 : 56 : 1],
[6660 : 68033 : 64]
3.14998723917251,
7.50417241238685
[3, 56] 3109
3110 [0, 0, 0, 0, 3110]
0
4178347200
{O}
-
0 - - - 3110
3111 [0, 0, 0, 0, 3111]
0
4181034672
{O}
-
0 - - - 3111
3112 [0, 0, 0, 0, 3112]
0
261482688
{O}
-
0 - - - 3112
3113 [0, 0, 0, 0, 3113]
0
348867684
{O}
-
2 [-8 : 51 : 1],
[136 : 1587 : 1]
2.16545834978931,
3.96743418709122
[-8, 51], [136, 1587] 3113
3114 [0, 0, 0, 0, 3114]
0
465455808
{O}
-
0 - - - 3114
3115 [0, 0, 0, 0, 3115]
0
1397264400
{O}
-
1 [9 : 62 : 1] 3.21682530796331
[9, 62] 3115
3116 [0, 0, 0, 0, 3116]
0
262155312
{O}
-
1 [-10 : 46 : 1] 2.49897399257434
[-10, 46] 3116
3117 [0, 0, 0, 0, 3117]
0
1049294412
{O}
-
0 - - - 3117
3118 [0, 0, 0, 0, 3118]
0
4199871168
{O}
-
1 [27 : 151 : 1] 3.64156204441145
[27, 151] 3118
3119 [0, 0, 0, 0, 3119]
0
4202565552
{O}
-
0 - - - 3119
3120 [0, 0, 0, 0, 3120]
0
16426800
{O}
-
0 - - - 3120
3121 [0, 0, 0, 0, 3121]
0
1051989228
{O}
-
1 [2064 : 18109 : 27] 6.19007595495882
- 3121
3122 [0, 0, 0, 0, 3122]
0
1403551296
{O}
-
1 [2 : 447 : 8] 3.98120810821566
- 3122
3123 [0, 0, 0, 0, 3123]
0
468150192
{O}
-
1 [2379 : 22382 : 27] 6.77839168555146
- 3123
3124 [0, 0, 0, 0, 3124]
0
21958596
{O}
-
2 [5 : 57 : 1],
[45 : 307 : 1]
2.61618115239378,
4.01000654857562
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1 [22417336643 : 123616139031 : 1548816893] 16.9045235130940
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1 [23588054264 : -240025294027 : 4034866688] 17.9401319403529
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1 [106573 : -572677 : 4913] 9.19083299861468
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1 [3270033 : -93272626 : 1601613] 12.6983371965679
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1 [188617904595258043094 : 1773604976738839215883 : 2145201638245016408] 32.7263278629614
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1 [-5160 : 209071 : 3375] 8.16865124234837
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1 [-15416499861 : -53133801146 : 1228480911] 17.2287772851160
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1 [-2 : 62 : 1] 2.52339780031425
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1 [2660 : 17603 : 64] 6.73707196451102
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1 [413170762302386853 : -2298184827951573332 : 16839617943407013] 28.5202124627317
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1 [158 : 1987 : 1] 4.66166351430466
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3918 [0, 0, 0, 0, 3918]
0
6631512768
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-
1 [3606 : 19997 : 216] 7.01538310304751
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3919 [0, 0, 0, 0, 3919]
0
6634898352
{O}
-
1 [62348021778164292173375790 : -1556317291634571040633959887 : 24810354179984822912011576] 42.2064035205045
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3920 [0, 0, 0, 0, 3920]
0
33075
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0 - - - 3920
3921 [0, 0, 0, 0, 3921]
0
1660418028
{O}
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1 [70 : 589 : 1] 3.92623464305553
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3922 [0, 0, 0, 0, 3922]
0
6645060288
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2 [-126 : 31 : 8],
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4.69355555018446,
5.41782568283060
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0
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1 [17 : 94 : 1] 3.43906541094822
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3924 [0, 0, 0, 0, 3924]
0
11548332
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1 [-126 : 33 : 8] 3.96129552377592
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3925 [0, 0, 0, 0, 3925]
0
22184100
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1 [94523 : -635094 : 2197] 8.57273596521706
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0
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1 [9104 : 257005 : 4096] 8.76901722411249
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0
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1 [289176 : 1581049 : 13824] 9.88639650853861
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0
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1 [282 : 4736 : 1] 4.98319337434855
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0
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{O}
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1 [416 : 8485 : 1] 5.59192289633393
[416, 8485] 3929
3930 [0, 0, 0, 0, 3930]
0
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{O}
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0 - - - 3930
3931 [0, 0, 0, 0, 3931]
0
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2 [651 : 21524 : 343],
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7.11516899774519,
15.5925286773076
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1 [-11 : 51 : 1] 2.72175798846067
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{O}
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0 - - - 3933
3934 [0, 0, 0, 0, 3934]
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1 [-9378110 : -51074199 : 941192] 11.8844354058563
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3935 [0, 0, 0, 0, 3935]
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1 [221 : 3286 : 1] 5.44214413186787
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1 [711953810 : -7045227979 : 7301384] 15.2157553931956
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3937 [0, 0, 0, 0, 3937]
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{O}
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2 [-6 : 61 : 1],
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2.77724200083999,
2.81677612433017
[-12, 47], [-6, 61], [342, 6325] 3937
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0 - - - 3938
3939 [0, 0, 0, 0, 3939]
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0 - - - 3939
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104784300
{O}
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1 [-3306 : 4067 : 216] 6.88851259735847
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3941 [0, 0, 0, 0, 3941]
0
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2 [67 : 552 : 1],
[-110 : 293 : 8]
3.80184938803717,
4.67896192696853
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3942 [0, 0, 0, 0, 3942]
0
9208512
{O}
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1 [3 : 63 : 1] 1.76320150891783
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3943 [0, 0, 0, 0, 3943]
0
2238803856
{O}
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1 [-7 : 60 : 1] 2.69608239742505
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3944 [0, 0, 0, 0, 3944]
0
419988672
{O}
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1 [86 : 800 : 1] 3.87491424659657
[86, 800] 3944
3945 [0, 0, 0, 0, 3945]
0
1680806700
{O}
-
0 - - - 3945
3946 [0, 0, 0, 0, 3946]
0
6726635712
{O}
-
1 [73103957630976 : -843704818225099 : 549755813888] 22.9852828800598
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3947 [0, 0, 0, 0, 3947]
0
6730045488
{O}
-
0 - - - 3947
3948 [0, 0, 0, 0, 3948]
0
420841008
{O}
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0 - - - 3948
3949 [0, 0, 0, 0, 3949]
0
1684216908
{O}
-
1 [-7800 : 10409 : 512] 7.46396963061303
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3950 [0, 0, 0, 0, 3950]
0
89870400
{O}
-
0 - - - 3950
3951 [0, 0, 0, 0, 3951]
0
749299248
{O}
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2 [-15 : 24 : 1],
[290 : 1817 : 8]
2.57094185918726,
5.25262140203182
[-15, 24] 3951
3952 [0, 0, 0, 0, 3952]
0
8785296
{O}
-
1 [13251 : 293561 : 27] 8.41303305493896
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3953 [0, 0, 0, 0, 3953]
0
1687630572
{O}
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2 [122 : 1349 : 1],
[1254 : 8713 : 27]
4.42189674106458,
5.78678813737393
[122, 1349] 3953
3954 [0, 0, 0, 0, 3954]
0
6753938112
{O}
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1 [-12678981839 : -40632046945 : 973242271] 17.0854480872950
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3955 [0, 0, 0, 0, 3955]
0
6757354800
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1 [110041186295703 : 1819808112153646 : 402437650887] 23.4605350937606
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3956 [0, 0, 0, 0, 3956]
0
105637068
{O}
-
1 [2824 : 32879 : 512] 7.40396677971238
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3957 [0, 0, 0, 0, 3957]
0
1691047692
{O}
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3 [19 : 104 : 1],
[-46 : 491 : 8],
[943 : 28958 : 1]
3.48682098982150,
4.62597004016360,
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[19, 104], [943, 28958] 3957
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0
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2 [171 : 2237 : 1],
[674157 : -3714511 : 29791]
5.19865469357015,
10.4395457660853
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3959 [0, 0, 0, 0, 3959]
0
2257010064
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1 [902717504944969 : 5069649243036208 : 56698339857713] 24.5292482966464
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3960 [0, 0, 0, 0, 3960]
0
47044800
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1 [34 : 208 : 1] 3.12841540993829
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3961 [0, 0, 0, 0, 3961]
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{O}
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2 [2 : 63 : 1],
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2.21473477373581,
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[-13, 42], [2, 63], [60, 469] 3961
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0
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{O}
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1 [23 : 127 : 1] 3.58034367782858
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0
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1 [208961544 : -1355569327 : 18399744] 14.4760002960912
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3964 [0, 0, 0, 0, 3964]
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1 [21 : 115 : 1] 3.53379111495584
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3965 [0, 0, 0, 0, 3965]
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1 [14980214 : -617388329 : 9800344] 13.9573125900538
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0 - - - 3966
3967 [0, 0, 0, 0, 3967]
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2 [516 : 4289 : 64],
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1 [1 : 63 : 1] 2.67543221280610
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[0, 63]
2 [-14 : 35 : 1],
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1.53736535592151,
3.23699038461237
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1 [-1 : 63 : 1] 2.67555806034549
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1 [5 : 64 : 1] 3.24216043391622
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0 - - - 3972
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2 [-126 : 65 : 8],
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4.69731175476052,
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0 - - - 3974
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1 [25 : 140 : 1] 2.55399200743236
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2 [30 : 176 : 1],
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2 [-2 : 63 : 1],
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2.21573846447361,
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[-2, 63], [8, 67], [163, 2082] 3977
3978 [0, 0, 0, 0, 3978]
0
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{O}
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2 [-9 : 57 : 1],
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2.52828340995481,
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0
2279871504
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1 [41 : 270 : 1] 3.40759504796597
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3980 [0, 0, 0, 0, 3980]
0
427690800
{O}
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1 [14 : 82 : 1] 2.68345042699629
[14, 82] 3980
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0
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{O}
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2 [139 : 1640 : 1],
[-54622387 : 320212618 : 5735339]
5.00478144833721,
13.6392262645406
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3982 [0, 0, 0, 0, 3982]
0
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1 [178365071773037590074063 : 5180166648875375392968313 : 211468097348360420021] 37.9494756427213
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3983 [0, 0, 0, 0, 3983]
0
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2 [226 : 1303 : 8],
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5.08656235777857,
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0
1674027
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0 - - - 3984
3985 [0, 0, 0, 0, 3985]
0
1715064300
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1 [-5082 : 9283 : 343] 6.73411811595182
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3986 [0, 0, 0, 0, 3986]
0
2287900224
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1 [79 : 705 : 1] 3.94451024195344
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1 [-46003209 : 97884100 : 3176523] 13.2827519995386
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3988 [0, 0, 0, 0, 3988]
0
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{O}
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2 [101 : 1017 : 1],
[-321 : 1297 : 27]
4.16284137991871,
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[101, 1017] 3988
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0 - - - 3989
3990 [0, 0, 0, 0, 3990]
0
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1 [-11369603338884051 : 214404572893987349 : 3410153852248359] 27.0756694089007
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3991 [0, 0, 0, 0, 3991]
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1 [28227255 : -170780492 : 857375] 12.9080597656793
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3993 [0, 0, 0, 0, 3993]
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1 [22 : 121 : 1] 0.69833353604246
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3994 [0, 0, 0, 0, 3994]
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{O}
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0 - - - 3994
3995 [0, 0, 0, 0, 3995]
0
2298243600
{O}
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1 [89 : 842 : 1] 4.59895087399390
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591408
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1 [-3 : 63 : 1] 1.76657161970264
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{O}
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0 - - - 3997
3998 [0, 0, 0, 0, 3998]
0
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{O}
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1 [11 : 73 : 1] 3.32015175809388
[11, 73] 3998
3999 [0, 0, 0, 0, 3999]
0
6908544432
{O}
-
1 [261307 : -1670164 : 6859] 9.79208614145113
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4000 [0, 0, 0, 0, 4000]
0
43200
{O}
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1 [-15 : 25 : 1] 1.69752726465998
[-15, 25] 4000

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Last Update: 2021.08.31
H.Nakao

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