1.Introduction

We searched the rational solutions of y^2 = x^3-n^2x.
This equation is related to the congruent number problem. 
About n= 5,6,7 mod 8, Elkies[2] actually showed there are rational solutions for n<10^6.
However, there seem to be few results about n= 1,2,3 mod 8.
According to Rubin and Silverbrg[1], if Parity conjecture holds and n= 1,2,3 mod 8, then analytic rank is even.
Hence if L(E(d),1)=0 then n is a congruent number.
Actually, rank appears only 2. We don't know whether there is a n such that rank >= 4.
 
     

2. Search results

 n is squarefree
 n=1,2,3 mod 8
 n < 10000.

 n  rank  [x, y]

[34 2 (-16 , 120 ), (-2 , 48 )] 
[41 2 (-9 , 120 ), (841 , 24360 )] 
[65 2 (-25 , 300 ), (-16 , 252 )] 
[137 2 (-3136/25 , -77112/125 ), (188502273/1073296 , 1619389601535/1111934656 )] 
[138 2 (150 , 720 ), (162 , 1080 )] 
[145 2 (-144 , 204 ), (-100 , 1050 )] 
[154 2 (-98 , 1176 ), (350 , 5880 )] 
[161 2 (-63 , 1176 ), (289 , 4080 )] 
[194 2 (-144 , 1560 ), (488977/144 , -341367929/1728 )] 
[210 2 (-150 , 1800 ), (-90 , 1800 )] 
[219 2 (-144 , 1980 ), (507 , 10296 )] 
[226 2 (-98 , 2016 ), (189953/784 , 29841153/21952 )] 
[257 2 (-1345380608/119617969 , -1126512029694480/1308261726953 ), (6016113/10816 , -13086618615/1124864 )] 
[265 2 (-225 , 2100 ), (-1296/25 , 233892/125 )] 
[291 2 (-3 , 504 ), (2883 , 154008 )] 
[299 2 (637 , 14196 ), (28561/36 , 4470895/216 )] 
[313 2 (-25 , 1560 ), (44337951203241447937/510401897989776 , 295230085612717493735175912065/11531038469929266614976 )] 
[323 2 (7225/16 , 429165/64 ), (1560753/64 , -1949679255/512 )] 
[330 2 (-275 , 3025 ), (-150 , 3600 )] 
[353 2 (-225 , 4080 ), (351422011199206017/886404376231936 , 94831871765904367939396545/26390513293157868765184 )] 
[371 2 (-196 , 4410 ), (-2597/961 , 18168612/29791 )] 
[386 2 (-98 , 3696 ), (614948915137/112896 , 482234812026220961/37933056 )] 
[395 2 (7205116/18225 , 804801914/2460375 ), (405 , 1800 )] 
[410 2 (-400 , 1800 ), (1210 , 39600 )] 
[426 2 (588 , 9828 ), (726 , 15840 )] 
[434 2 (448 , 2352 ), (722 , 15504 )] 
[442 2 (-16250/49 , -1825200/343 ), (2057/4 , 47685/8 )] 
[457 2 (-61987021749648/255968200489 , -781047485604259136340/129502759578001237 ), (29252113/41616 , 120208263175/8489664 )] 
[465 2 (-1815/4 , 17325/8 ), (-15 , 1800 )] 
[505 2 (-28224/169 , -13531224/2197 ), (-100 , 4950 )] 
[514 2 (-64 , 4080 ), (7145763953/12082576 , 298776203813367/41999034176 )] 
[546 2 (-507 , 4563 ), (-468 , 6084 )] 
[561 2 (-528 , 4356 ), (-272 , 8092 )] 
[602 2 (-98 , 5880 ), (2872926/4225 , -2264271576/274625 )] 
[609 2 (-567 , 5292 ), (-441 , 8820 )] 
[651 2 (-525 , 8820 ), (-363 , 10296 )] 
[658 2 (1458 , 49680 ), (1792 , 70560 )] 
[674 2 (-576 , 8400 ), (1504627153/1382976 , 45815080051943/1626379776 )] 
[689 2 (-400 , 11220 ), (231361/324 , 29232775/5832 )] 
[721 2 (59248/81 , 2429812/729 ), (847 , 12936 )] 
[723 2 (-32400/169 , -21206340/2197 ), (2237494369/102400 , 105780363172847/32768000 )] 
[731 2 (48841/64 , 3099525/512 ), (25857/16 , -3708159/64 )] 
[761 2 (-1600/841 , 25599960/24389 ), (1902165921/672400 , 79902649977969/551368000 )] 
[777 2 (-567/4 , 72765/8 ), (-2775/289 , 11828160/4913 )] 
[793 2 (-17424/25 , -1248324/125 ), (7102225/2916 , 17896117265/157464 )] 
[866 2 (-578 , 15504 ), (2296549297/1498176 , 90810454453271/1833767424 )] 
[889 2 (-7 , 2352 ), (308412769/90000 , 5230813038353/27000000 )] 
[890 2 (-90 , 8400 ), (64881/64 , -7913079/512 )] 
[905 2 (-900 , 2850 ), (-906304/2809 , -2261098056/148877 )] 
[915 2 (-900 , 4950 ), (960 , 9000 )] 
[985 2 (-166464/169 , -235416/2197 ), (-59028489/235225 , -1721385769116/114084125 )] 
[987 2 (331632/289 , 97416900/4913 ), (3388 , -188650 )] 
[995 2 (2205 , 92400 ), (198025/4 , 88103325/8 )] 
[1003 2 (67473/16 , 17023545/64 ), (288747157793/35344 , 155158857773747535/6644672 )] 
[1057 2 (-776223/1936 , -1668168495/85184 ), (64486513/9216 , -511906733065/884736 )] 
[1073 2 (-870958144/2146225 , -62915110482504/3144219625 ), (567617/196 , 397208505/2744 )] 
[1081 2 (-2783/144 , 8210609/1728 ), (1369 , 31080 )] 
[1105 2 (-576 , 22632 ), (-169 , 14196 )] 
[1113 2 (-63 , 8820 ), (3588592/9 , 6798051260/27 )] 
[1122 2 (-578 , 23120 ), (-528/49 , 1263240/343 )] 
[1131 2 (-83607/196 , -59363667/2744 ), (-117 , 12168 )] 
[1145 2 (-2704/25 , 1481844/125 ), (555025/484 , 22808175/10648 )] 
[1146 2 (303117/169 , 128376639/2197 ), (2028 , 75348 )] 
[1154 2 (-2 , 1632 ), (129376173303457/35431285824 , 1396148942587626223759/6669301793223168 )] 
[1155 2 (-605 , 24200 ), (-539 , 23716 )] 
[1169 2 (1178352/841 , 705145476/24389 ), (2743094132289/78145600 , 4540671702332930913/690807104000 )] 
[1178 2 (1900 , 64980 ), (22941702/5041 , 106140064800/357911 )] 
[1185 2 (-4335/4 , -126225/8 ), (-735 , 25200 )] 
[1186 2 (-16972951554/29866225 , -4050418841660256/163218919625 ), (39167057/18496 , 203069912871/2515456 )] 
[1195 2 (93697560000/60855601 , 18085024345509000/474734543401 ), (115676/49 , 33929874/343 )] 
[1201 2 (-49 , 8400 ), (441146338386879699361/8002812487233600 , 9263410655305500559760823366641/715919120720437771584000 )] 
[1217 2 (-2262016/4225 , -6944775648/274625 ), (155154966420033/88461035776 , 1391690347616564507295/26310435104641024 )] 
[1241 2 (-441 , 24360 ), (2809 , 133560 )] 
[1249 2 (6497887039943159329/2523567281414400 , 14484568564308881477258907983/126771705209926153728000 ), (450840289/101761 , 9184412287440/32461759 )] 
[1282 2 (-400 , 24360 ), (893241052160081/12638256400 , 26692027010740968349479/1420792784488000 )] 
[1321 2 (1874437654081/732243600 , 2198189348404309729/19814511816000 ), (24119516809/829921 , 3742000167255120/756058031 )] 
[1330 2 (-630 , 29400 ), (-2366/9 , 570752/27 )] 
[1339 2 (119068/81 , 16953182/729 ), (142129/36 , 50406785/216 )] 
[1346 2 (38442433/28224 , -36480260447/4741632 ), (130896481/1764 , 1497340245745/74088 )] 
[1379 2 (-196 , 19110 ), (10726865212/7634169 , 213188912401654/21093208947 )] 
[1387 2 (-831744/625 , -222786096/15625 ), (120164497/82944 , -380450819015/23887872 )] 
[1393 2 (676731937/484416 , 1332205558705/337153536 ), (20805232/3249 , 92625822100/185193 )] 
[1411 2 (395641/256 , 101530035/4096 ), (106097/16 , -33767049/64 )] 
[1419 2 (-507408/361 , -50098356/6859 ), (-363 , 26136 )] 
[1434 2 (2409598/1521 , 1589791672/59319 ), (5766 , 424080 )] 
[1443 2 (-507 , 30420 ), (5702817289/3610000 , 175258799307163/6859000000 )] 
[1482 2 (-468 , 30420 ), (-507/49 , 1635075/343 )] 
[1513 2 (-1225 , 31080 ), (-1088 , 34680 )] 
[1561 2 (23754987361/5475600 , 3416054450577391/12812904000 ), (94192/9 , 28584836/27 )] 
[1595 2 (-605 , 36300 ), (3115225/1444 , 3702290475/54872 )] 
[1610 2 (-1035 , 39675 ), (-810 , 39600 )] 
[1633 2 (-947807/1296 , -1842223985/46656 ), (41860271377/2509056 , 8523395609507065/3974344704 )] 
[1635 2 (-900 , 40950 ), (-42135/1444 , -484548525/54872 )] 
[1649 2 (-1600 , 15960 ), (356555025/135424 , 5248642558215/49836032 )] 
[1651 2 (343408/81 , 185354468/729 ), (138420372892/5433561 , 51390879933421666/12665630691 )] 
[1659 2 (-507 , 35568 ), (2541 , 97020 )] 
[1705 2 (-495 , 36300 ), (7225/4 , 202725/8 )] 
[1731 2 (-144 , 20700 ), (1773126193/1024144 , 1446805227223/1036433728 )] 
[1745 2 (-900 , 44850 ), (-321616020544/2188087729 , -2157659144941632696/102352179699433 )] 
[1762 2 (-1600 , 29520 ), (15879179254973783041174105892561/2126126513211571474489600 , 63276444026070360037534763694982914139714739559/3100156762193113624646710756461056000 )] 
[1770 2 (-1470 , 37800 ), (-150 , 21600 )] 
[1785 2 (-1764 , 11466 ), (-735 , 44100 )] 
[1794 2 (-1587 , 33327 ), (-2783/16 , 1507121/64 )] 
[1858 2 (-1058 , 49680 ), (1391452784096300146894649025329/549187271742385625187216400 , 1115918450440935227623625306166152809761439017/12870063653273048739782237250435660712000 )] 
[1939 2 (-1764 , 33810 ), (125692/9 , -44130086/27 )] 
[1995 2 (-1805 , 36100 ), (-1680 , 44100 )] 
[2035 2 (-1936 , 27588 ), (14985/4 , 1540125/8 )] 
[2059 2 (6475484/3025 , -4507773102/166375 ), (44102881/4900 , 285120503529/343000 )] 
[2113 2 (-130498038693843296832/65205163291002289 , -504862479519988753507845465960/16650335170335083450055913 ), (27035684977/2143296 , 4382538916027895/3137785344 )] 
[2130 2 (2205 , 26775 ), (3750 , 189000 )] 
[2139 2 (-1587 , 57132 ), (3100 , -124930 )] 
[2145 2 (-1911 , 42588 ), (-1089 , 60984 )] 
[2154 2 (2178 , 15048 ), (27840829822/10673289 , 2620004252103784/34869635163 )] 
[2170 2 (2205 , 18375 ), (2366 , 45864 )] 
[2195 2 (2645 , 75900 ), (252442735600/89510521 , 79640077284513900/846859039181 )] 
[2201 2 (-93775/64 , -32188695/512 ), (4358334363201/575040400 , 8706621888719476449/13789468792000 )] 
[2249 2 (-472105984/319225 , -11752207244064/180362125 ), (-676 , 55770 )] 
[2257 2 (-665856/625 , -1014763728/15625 ), (265533793/79524 , 3188747322775/22425768 )] 
[2273 2 (-672605329070767208508992/506534848025509722095329 , -944254019949304544730667129953604680360/360507241873054627146414824781537233 ), (5943188097/430336 , 451924635574335/282300416 )] 
[2282 2 (-120127/64 , -28789215/512 ), (66654/25 , -8898792/125 )] 
[2298 2 (718125/121 , 561085425/1331 ), (11355025444894/13727025 , 38263129866249534728/50858627625 )] 
[2306 2 (-23363075331650/20037251809 , -192684927946988986080/2836333105319377 ), (240802897/76176 , 2555920413991/21024576 )] 
[2329 2 (-272 , 38148 ), (2873 , 90168 )] 
[2337 2 (-1025 , 67240 ), (15957509067225/4410553744 , 48662787529051192035/292913695246528 )] 
[2379 2 (-1296 , 71820 ), (48841/4 , 10587005/8 )] 
[2418 2 (-507 , 53235 ), (-227850/4489 , -5180059080/300763 )] 
[2434 2 (-1922 , 65472 ), (33975329914798193450323936080257/467640880287830840781201664 , 197925461379951615136437693469259649460379434431/10112736796525143045886109425847191539712 )] 
[2465 2 (-784 , 65436 ), (-289 , 41616 )] 
[2530 2 (-2420 , 36300 ), (-414 , 50784 )] 
[2569 2 (129848774363329/9789123600 , 1451626976260677948767/968535888984000 ), (1150912/81 , 1214356024/729 )] 
[2594 2 (-144 , 31080 ), (60055929365233/4790854656 , 455334417193813420087/331603795869696 )] 
[2611 2 (-1764 , 80850 ), (119861308/8649 , 1288755069238/804357 )] 
[2698 2 (163229/25 , 60053433/125 ), (1206360040222/84989961 , 1300842438399656200/783522450459 )] 
[2706 2 (-1650 , 87120 ), (-528 , 60984 )] 
[2730 2 (-2366 , 66248 ), (-1680 , 88200 )] 
[2777 2 (-129426808889606466360848/56862279509046336649 , -32544167522852158992316207237818180/428781854919479666060082345893 ), (22360442599379588749272990194383510246691073/197887896618551139767536841724488924176 , 105703507671862230131667256629805782953962081428795860357285060865/2783741144681036102578868822382006245473186568821468096576 )] 
[2810 2 (-1600 , 92400 ), (1300131081/240100 , 40073085644229/117649000 )] 
[2818 2 (-107407757682924955218/360259425520390201 , -10462364911514183090676285407760/216233525026800927421555949 ), (794677409/78400 , 21518824065423/21952000 )] 
[2833 2 (-44195598292892746752/15965109164790769 , -63912437706278122312912772640/2017241242356143656813897 ), (106988627276114093377/188398024865856 , 1106626379940490178219567310305/2585916624072164138496 )] 
[2849 2 (-135247/64 , -44973033/512 ), (3388 , 106722 )] 
[2865 2 (34039065/6724 , 163729464075/551368 ), (3257340/121 , 5845492350/1331 )] 
[2914 2 (-45167/196 , -121002393/2744 ), (3577647473/3136 , 213990700454007/175616 )] 
[2929 2 (-9239054400/116143729 , -32686518924595080/1251680967433 ), (24255049/100 , 119445987843/1000 )] 
[2945 2 (-31/16 , 262353/64 ), (21025/4 , 2525175/8 )] 
[2953 2 (-343672927632/130256569 , -101272598056305300/1486618221997 ), (30842067034746694674585697/400320205016396418576 , 171157512830421675856140380335859275375/8009608072696462020649587061824 )] 
[2995 2 (389578193508956/110598148969 , -4047451900856326750446/36780852215577547 ), (2156400/121 , 3121568700/1331 )] 
[3001 2 (-32680890000/12880921 , -3732183178610700/46229625469 ), (14297100923642660401/4743834500250000 , 4982455818602072127298980649/326733973121968875000000 )] 
[3003 2 (-1053 , 91260 ), (-77/9 , 237160/27 )] 
[3017 2 (-567 , 70560 ), (43077562775740846889971871545571553/10985510791560253808335028332816 , -5711242214010014124141487970295215674145035219428945/36410813534180594960284879625253572126505356864 )] 
[3018 2 (26366599509694/6841771225 , 84192371840775978872/565917106875875 ), (7350 , 574560 )] 
[3026 2 (5202 , 305184 ), (140777/4 , 52624299/8 )] 
[3081 2 (-975 , 91260 ), (6558721/2116 , 1836608345/97336 )] 
[3090 2 (-136890/49 , -23938200/343 ), (-150 , 37800 )] 
[3099 2 (-576 , 73080 ), (5057506888753/23970816 , 11372550435323158697/117361115136 )] 
[3122 2 (-223/16 , 745935/64 ), (9469626624409/2816424900 , 10818327434716089827/149467669443000 )] 
[3129 2 (-3540687/1444 , -5281551297/54872 ), (54208/9 , 10784312/27 )] 
[3145 2 (-2601 , 90168 ), (-11664/169 , -57388716/2197 )] 
[3161 2 (-30276/625 , -343718382/15625 ), (45657049/2500 , 303848444907/125000 )] 
[3171 2 (-5103/4 , -829521/8 ), (12564843484/469225 , 1398521087108398/321419125 )] 
[3265 2 (-156816/289 , -368463348/4913 ), (93412225/15129 , 766274254300/1860867 )] 
[3281 2 (-81 , 29520 ), (36173025/7744 , -154853963985/681472 )] 
[3289 2 (-497783/324 , -664776541/5832 ), (950521/36 , 919489285/216 )] 
[3290 2 (-90 , 31200 ), (-35/9 , 175175/27 )] 
[3355 2 (-193919/22500 , -33241743271/3375000 ), (21025/4 , 2346825/8 )] 
[3379 2 (-7978662048243549375/16251649105585936 , -153467918414801623509852297825/2071792016205745647370816 ), (77500/9 , -19844650/27 )] 
[3409 2 (-63/1936 , 52384479/85184 ), (4762000140625/1360724544 , 2349304216615617625/50194406979072 )] 
[3433 2 (-520906869589392/297632440249 , -20062188326164112176620/162375461204923693 ), (3895275606949601389589588437433348505418094693377/326124040674205430342421770633370068275005456 , 7363496712095964194190887083793249376480111018243195741126129548489902465/5889442986359488670718229857719060317999459462304397658030735831104 )] 
[3434 2 (243049/64 , 51166005/512 ), (166617/4 , -67779459/8 )] 
[3435 2 (-900 , 99450 ), (-734233948977544634535/855977501998632484 , -77148039860830728247647931706475/791942271894370831158116648 )] 
[3443 2 (-17424/25 , -11126676/125 ), (283814197681447423681302577/50993390267135263388736 , -3756704414451554503687441713943642656425/11515182627232564979899080826473984 )] 
[3458 2 (-2275 , 124215 ), (192178350/32041 , 2176791358560/5735339 )] 
[3554 2 (-417698/289 , -606442656/4913 ), (1404400417/138384 , 49297609403441/51478848 )] 
[3570 2 (-2499 , 127449 ), (-2100 , 132300 )] 
[3593 2 (-2025 , -133560 ), ()] 
[3594 2 (1511277/121 , 1779294159/1331 ), (3825656062/182329 , 233126968494104/77854483 )] 
[3595 2 (13875625/3364 , 25340485875/195112 ), (14186850716/667489 , 1665428026662786/545338513 )] 
[3601 2 (-2214144/625 , -600531504/15625 ), (1338649/324 , 759344885/5832 )] 
[3603 2 (-3600 , -8820 ), (150424353168831054554161/12270959817929280400 , 55764565420221600086956164841804841/42985086100068347377651592000 )] 
[3634 2 (245134/49 , 83412720/343 ), (4013753/196 , 7913669133/2744 )] 
[3674 2 (409150/81 , 179605160/729 ), (377542/49 , 203907264/343 )] 
[3705 2 (-95 , 36100 ), (30780 , 5360850 )] 
[3713 2 (-4472788309361775/1514396049664 , -227896783713703586867385/1863627893884915712 ), (14736897/256 , -56455181055/4096 )] 
[3746 2 (-130089023954/35581225 , -10468019561959344/212242007125 ), (2278708657/112896 , 106886267245801/37933056 )] 
[3761 2 (-22568524744256/34486347025 , -606772764855651117528/6404287074277625 ), (359280418948370609022971395244000724691206652713921/47452193227300198362025174664198962187636353600 , 5910452257930463090271683363470147063665983355405248768385946221362852264031/10336760057193814019273190623665693892714645759291675014276715790784000 )] 
[3778 2 (-578 , 89760 ), (20964882393279190597693696824464739809/1198979701879709770025436748825600 , -93725381709733985821121185025233048420182410092164705873/41516214406999138214063831787353997326963716096000 )] 
[3794 2 (20125273/4356 , 51521285053/287496 ), (21294 , 3057600 )] 
[3841 2 (-2783 , 139656 ), (5199863194399418881/1245948804000000 , 4637387008305402769026433279/43979500883592000000000 )] 
[3842 2 (3690241/900 , 2476151711/27000 ), (6217126321/3600 , 490211463140119/216000 )] 
[3865 2 (-2944656/841 , -2361931572/24389 ), (715913544896058265/9170734135684 , 605003566944746911514908725/27771935939242842248 )] 
[3881 2 (-12318953088496400/3672240183481 , -795439848919656893227620/7037146913766291629 ), (48071542666325121/11083972147600 , 4704582229645392382608831/36901425112118776000 )] 
[3882 2 (386988127381725/7587977881 , 7590749902416357314265/660981165236029 ), (1771486/25 , -2354257016/125 )] 
[3899 2 (-20206207/8464 , -117286256577/778688 ), (12682012/3249 , 2133677854/185193 )] 
[3930 2 (-1470/169 , 25464600/2197 ), (515205/121 , 142307325/1331 )] 
[3939 2 (-117 , 42588 ), (5536609/1156 , 7410949975/39304 )] 
[3985 2 (-451584/5329 , -14267408736/389017 ), (247275625/62001 , 156998714500/15438249 )] 
[4002 2 (-103247/64 , -75316375/512 ), (6525 , 416295 )] 
[4010 2 (-400 , 79800 ), (271722797361/66846976 , -23189555250362409/546540875776 )] 
[4017 2 (-975 , 121680 ), (-5620651001703/39542913316 , -376349850794020385205/7863266484539864 )] 
[4033 2 (-21773462087806328881959012/5399831698953898331161 , -1961916391004982749300850546951867030/396798787149546591414051589449091 ), (18104137/1764 , 70834462595/74088 )] 
[4121 2 (-2689600/841 , -3584648040/24389 ), (2741188981401/157904356 , 4408727883994903755/1984226137496 )] 
[4123 2 (451612/81 , -204301090/729 ), (219343600/1089 , 3247853586740/35937 )] 
[4154 2 (-1922 , 161448 ), (3308382/529 , 4498425624/12167 )] 
[4179 2 (-1587 , 154008 ), (-145071/676 , -1074573135/17576 )] 
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[7793 2 (-182206851892860829063232/33408557135264769649 , -79381951890534558490938976676601720/193101914364347508225233838857 ), (1233953815991294488740825085857/157864990302298586417190976 , 106239962077197000822656850787011059069210865/1983484179707515811493031112316264308224 )] 
[7795 2 (359193600/44521 , 1755779474400/9393931 ), (1278898120061756/21394620361 , 45345024354587484105354/3129369725583109 )] 
[7819 2 (-1695204/841 , -8272276530/24389 ), (233510488271452/27243813249 , -1461710004861360131794/4496782083440193 )] 
[7874 2 (7639547713/968256 , 42513578472673/952763904 ), (11093598 , 36949496688 )] 
[7881 2 (3845521/484 , 957389615/10648 ), (13620924/529 , 47857489650/12167 )] 
[7995 2 (-6084 , -404586 ), (15600 , 1673100 )] 
[8002 2 (-25529798342160969870061602/4199572491570202177201 , -110413277358192287375282721048571042080/272149551821487538906860250205801 ), (1502859756751158383178190747361/4801400238263181193446400 , 1841771355133996906315244474371055962113977391/10520875092172897490246232382066688000 )] 
[8090 2 (110607289/5776 , 1054351220013/438976 ), (63405867681/1449616 , 15690460371083121/1745337664 )] 
[8106 2 (-1834602/289 , -1973153952/4913 ), (69673/4 , -16277813/8 )] 
[8122 2 (-1922 , 345960 ), (21909892290487697311111794033147766622/1719925423692420760971889745032849 , 79007677990641956234999356224402029743079542642872657960/71328718964050842803520299170255613876232539704007 )] 
[8138 2 (-949040547338/230827249 , -1579259086181116080/3506958394057 ), (27521504377/12996 , 4565675566120915/1481544 )] 
[8162 2 (-6727/4 , -2620275/8 ), (13013 , 1156155 )] 
[8169 2 (-816900/289 , -2001976830/4913 ), (15508435327/146689 , 1925536045684636/56181887 )] 
[8170 2 (-11875/529 , -470969625/12167 ), (26109686/289 , 132867690384/4913 )] 
[8194 2 (-256 , 131040 ), (21167269313/614656 , 2991175443874143/481890304 )] 
[8234 2 (-51842/9 , -12056968/27 ), (5281316350/21609 , 383589459983080/3176523 )] 
[8241 2 (1803864249/218089 , 6544200845160/101847563 ), (282048225/256 , 4736667579345/4096 )] 
[8258 2 (9427006609/1040400, 376695741065273/1061208000 ), ()] 
[8313 2 (-31296/25 , -36346392/125 ), (44395911023433/4096512016 , 189785296889349327045/262193155072064 )] 
[8354 2 (-2304 , 385440 ), (38078177954400407466391488294337/3588060836770010696580722064 , 144909879052243216591243368079724645122632624289/214926366699964745827065137442821963335488 )] 
[8385 2 (-65 , 67600 ), (42268785/3364 , 204667242975/195112 )] 
[8393 2 (69345393975/7134241 , 9210883901745240/19055557711 ), (1386044/25 , 1612988322/125 )] 
[8498 2 (81127921545978684027721/5326261582872860100 , 19176966884543051970335129949602981/12292316602871380373828349000 ), (13384350/361 , 47662562640/6859 )] 
[8515 2 (34385/4 , 874575/8 ), (49052629665/5484964 , 3321089578223625/12845785688 )] 
[8521 2 (72607441/5929 , 444357538920/456533 ), (57320075830373915247221564913716531919096379681/3485983729507379589446722130959186027290000 , 11736908254608494064476339287910075299811941812909558103204243764465329/6508606770432710009588585098323478507904233050846652099317000000 )] 
[8547 2 (-528 , 196020 ), (51810297/5476 , 159941860155/405224 )] 
[8554 2 (-3146 , -446160 ), (1201886/25 , -1296609384/125 )] 
[8555 2 (34225/4 , 108225/8 ), (238918849/11236 , 3380894910393/1191016 )] 
[8571 2 (-1126176678705047222792448/140081053426303145209 , -441712435882095795039777069549366096/1657941103071952530124855533427 ), (49513435633/976144 , 10859110521784777/964430272 )] 
[8578 2 (-7434879655852471906332738/1109014129956205065121 , -16182456814629669003860891881330134240/36932237464825489975237674980081 ), (17310751409/883600 , 2047654429782423/830584000 )] 
[8593 2 (-4767626304/1918225 , -1089491592828744/2656741625 ), (20412599621007217/2324825968644 , 599120876367717004785185/3544750497778315272 )] 
[8601 2 (-144089129567/17172736 , -12325954964495887/71163817984 ), (15228 , 1550718 )] 
[8609 2 (-1600413356844857478780698624/384998954318742097312225 , -116113544762285607066653230491496409717376/238885244443748712071067132119404625 ), (386050986130689/44133606400 , 1343601653779033588863/9271588032512000 )] 
[8690 2 (87324941/9409 , 286545086289/912673 ), (133510 , 48679800 )] 
[8705 2 (-1430961427984/167365969 , -327529526582560764/2165213540953 ), (-108900/841 , -2415631350/24389 )] 
[8729 2 (-3520623406783/751637056 , -10388250583347128289/20606881527296 ), (-61103/36 , -76195441/216 )] 
[8762 2 (-234650/49 , -174164640/343 ), (478436775916297/46855797444 , 5373423257924890166075/10142499626323128 )] 
[8786 2 (34796953/1764 , -183779129827/74088 ), (3378286/49 , 6158702640/343 )] 
[8801 2 (-814048542679320898114585121/1037052465763977905117121 , -259372308636610706252382545881194675333760/1056090394678451715907636006372338081 ), (-676 , 228150 )] 
[8809 2 (15053063/1681 , 10497027408/68921 ), (172797705169/19184400 , 14985639165433447/84027672000 )] 
[8835 2 (-27735/4 , -3647475/8 ), (78585/4 , 19676475/8 )] 
[8859 2 (-179060618670655822992/4831459134020293369 , -572742290623101156233387280584028/10619827579970365960828256653 ), (10988113/256 , 35639494183/4096 )] 
[8866 2 (-494319103850/58018689 , -100048558580158760/441928354113 ), (-3627 , -487227 )] 
[8890 2 (-1690 , 358800 ), (-635/9 , 2016125/27 )] 
[8897 2 (-275807/256 , -1187349135/4096 ), (1393049278593/13075456 , 1638438251645190975/47280848896 )] 
[8906 2 (8487935497/427716 , 698821324149061/279726264 ), (168437353/2916 , 2159898125077/157464 )] 
[8931 2 (-7056 , -459900 ), (-507 , 200772 )] 
[8962 2 (-261295211656962/35645817601 , -2970868265599641072960/6729966008886401 ), (84874741237064321/3670136377600 , 22794533266636311016786881/7031100466750976000 )] 
[8970 2 (-1170 , 304200 ), (167670 , 68558400 )] 
[8979 2 (-512207424/58081 , -2219263932600/13997521 ), (835777/64 , -554807519/512 )] 
[9049 2 (-23951843457156879413904/2667133994732700025 , -459165709092698756446199498326644/4355793197069611497539906125 ), (499636694946446519208372573169/26540091241438855203536400 , 309693319419794002794115960011828304650090697/136726789870521188574517758756270888000 )] 
[9066 2 (28361932755838/1951253929 , 118062593059276470968/86192739805717 ), (8381517/169 , 23856331329/2197 )] 
[9089 2 (-7430094672400/1461762289 , -30022449059359796220/55887557595337 ), (-14884/25 , -27661914/125 )] 
[9121 2 (15231497983/1481089 , 868352983589832/1802485313 ), (457332056881/4161600 , 308209776882776279/8489664000 )] 
[9122 2 (-5959999890661615439762/22589169255723344521 , -15901266431307779194059270658217520/107361949587224473067937750181 ), (9902873341893869918401/226731031150352400 , 963734080797285615928278334863649/107960887174059642777768000 )] 
[9131 2 (-83642927/9216 , -84468083993/884736 ), (23092092/2401 , 34852903674/117649 )] 
[9170 2 (-9275455/1936 , -46101739425/85184 ), (-3275/9 , -4719275/27 )] 
[9226 2 (-1973727/256 , -1822448817/4096 ), (407484350/11449 , 7944411263880/1225043 )] 
[9257 2 (-3949312679024000585140073/72483798949862676954561 , -1333412271678409852819476052008168979600/19514679392049854784913676743713441 ), (282508531435775801040680418273/4259831484524595865374736 , -148687634292879426378733703577773723771415855/8792019216800569006064241628218449984 )] 
[9281 2 (-6390784/4225, -97803104736/274625 ), ()] 
[9339 2 (-8448 , -365904 ), (14658449403/833569 , 1503774597992472/761048497 )] 
[9345 2 (-1764 , 385434 ), (-1424 , 348524 )] 
[9347 2 (88959484528294750236/6597923814036025 , -604705080290800194615018103266/535933549386611694470125 ), (14524237/529 , 52046510880/12167 )] 
[9354 2 (22372566/529 , 103200672960/12167 ), (10853758/121 , 35562797992/1331 )] 
[9377 2 (-6635776/4225, -100613776368/274625 ), ()] 
[9379 2 (-295390179392/52664049 , -215157660249829528/382183003593 ), (18170513/1936 , 2903249223/85184 )] 
[9395 2 (27967036/2601 , 71933279734/132651 ), (8354636334579731551600/236213594499646201 , 736211161189116427356868274783100/114804082629102091781884301 )] 
[9401 2 (-1088/9 , 2790584/27 ), (92139201/400 , -883699631199/8000 )] 
[9434 2 (-937936213994/519703209 , -4660601243290403840/11847674055573 ), (23973129/2500 , 21035981883/125000 )] 
[9435 2 (-2242757775/1459264 , -643320231629175/1762790912 ), (-765 , 260100 )] 
[9442 2 (-6400, -555360 ), ()] 
[9451 2 (31452928/2601 , 110043966032/132651 ), (19998346239933803751963552278299894972/655971558742549645367793668349921 , 85025770120945404984312986152837773367537938474374873386/16800705333437754600494313537876447903145310419281 )] 
[9465 2 (-605602881/361201 , -82801939016628/217081801 ), (60045975775/4157521 , 11113773190865900/8477185319 )] 
[9483 2 (-25143/4 , -4503555/8 ), (1236649509312/95433361 , 937217096370427320/932288503609 )] 
[9490 2 (-1040 , 304200 ), (377213265/14884 , 6793210827975/1815848 )] 
[9497 2 (-12950509813231427934608/2075029109187953689 , -1690355853429387384429818279773740/2989071407647682059187584637 ), (1536212053576327467914434576593/3968843604635881418912656 , 1903469796429865402672410043835959630944646425/7906713061065320891651365390021338304 )] 
[9521 2 (-229818952050984604067840000/37310516753056223254561 , -4106427250938911176970314238002627363200/7206873450922831813717171669163441 ), (53283939211297857936325425327708174801/2012179526269617622025224088070400 , 362940666647073077069894981482222392712389046207072877799/90260989176486030694409311470988439461626875392000 )] 
[9546 2 (-1332 , 344988 ), (1777014732/165649 , 34176947588316/67419143 )] 
[9554 2 (-850 , 277440 ), (15953650/1089 , 48306627440/35937 )] 
[9579 2 (-33759/4 , -3329865/8 ), (20188 , -2524942 )] 
[9595 2 (-902500/169 , -1279835250/2197 ), (18705625/484 , 78368935125/10648 )] 
[9601 2 (-32626944/21025 , -1137869338704/3048625 ), (7503358355747674336185995600185976641/539605076013445148317567564185600 , 14867773462769143384265392333523594756910481877975486689/12534702752686035164176419065520674501510037504000 )] 
[9618 2 (-5082 , -582120 ), (7960417392/58081 , 708486806091240/13997521 )] 
[9634 2 (-3362 , -523488 ), (104944049758351976426872756730951013059353087553/4072837499764471650224119843675418024298256 , 31530996514547703739823795076909544139190351792331300180917550325070177/8219504244785408053272771224982309278493433940400111508237843904 )] 
[9641 2 (-51507151/6400 , -243822745257/512000 ), (281912481/19600 , -3512631161871/2744000 )] 
[9642 2 (44949924484894/1804975225 , 277860583351027404728/76684372434125 ), (401423578125/11703241 , 244078347576873375/40036787461 )] 
[9658 2 (265365955701/14938225 , 114731373202452699/57736239625 ), (23738394723998/10804369 , 115657240101913916280/35513960903 )] 
[9690 2 (-1140 , 324900 ), (24990 , 3641400 )] 
[9730 2 (-9841895/2116 , -56732735325/97336 ), (1851531430/2601 , 79662890396600/132651 )] 
[9731 2 (829548288/72361 , 12631203418512/19465109 ), (6902172/361 , 15609091554/6859 )] 
[9779 2 (-48223/16 , -32686479/64 ), (318400350625/2782224 , 179006556247058575/4640749632 )] 
[9809 2 (8170897/256 , 22226007111/4096 ), (114047212537/145161 , 38511741848669704/55306341 )] 
[9841 2 (-6084, -603330 ), ()] 
[9867 2 (-315887/36, -91304785/216),(4029025/324, 4921972055/5832) ] 
[9986 2 (-352238882/54289, -7734446666688/12649337 ), (55168506621817307377/1185702835249296, 400218062373704466099033912631/40828534114276327438656)] 


3.References

[1]. K. Rubin and A. Silverberg, Ranks of elliptic curves, Bull. Amer. Math. Soc. (N.S.) 39 (2002)
[2]. Noam Elkies, Curves D y^2 = x^3 - x of odd analytic rank
     http://www.math.harvard.edu/~elkies/antsv_cong.pdf



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