# Lists of S-integral points (x,y) on the Mordell curves # y^2 = x^3 + a, with the following constraints: # we consider only curves of rank r = 4, # a is bounded by |a| <= 10000, # S is the set of the first 300 primes. # It contains 18 curves in total. # It contains 3886 points in total. # For each point P, only one of +P, -P is listed. # Format of the points: "(P(x),P(y))". # Computing this list took 619074 seconds. # Authors: Rafael von Känel and Benjamin Matschke, 2015. # License: Creative commons 3.0 by-nc. # # a = -9967: # (32,151) (56,407) (98,965) (89/4,259/8) (232/9,2285/27) (199/9,784/27) (478/9,10097/27) (844/9,24371/27) (1052,34121) (1124/25,35557/125) (2186/25,101441/125) (1103/49,13012/343) (3662/169,31615/2197) (8218/9,744983/27) (7241/16,616133/64) (9542/361,632369/6859) (18866/121,2587903/1331) (13331/25,1539146/125) (16411/81,2101078/729) (50612/169,11384125/2197) (66508/729,17038907/19683) (72971,19711762) (162614/2809,63868151/148877) (172202/3721,67770889/226981) (104831/4225,20008604/274625) (195467,86419186) (319622/10201,148565959/1030301) (261673/10404,81810827/1061208) (501694/15129,302920489/1860867) (900032/22801,781620001/3442951) (1140134/9409,1213986931/912673) (1079009/784,1120822319/21952) (645809/28900,169611127/4913000) (1071523/2601,1109101490/132651) (763153/26244,514104857/4251528) (1783642/9801,2380138039/970299) (2196866/7921,3255396397/704969) (1041113/27556,959128765/4574296) (2764148/16129,4591044727/2048383) (2956858/8649,5083835977/804357) (3189908/19321,5690963275/2685619) (3381857/18496,6214103791/2515456) (3574928/165649,620130337/67419143) (7534676/10201,20681950853/1030301) (10874102/351649,29196170755/208527857) (18195556/4761,77615410267/328509) (12915134/508369,29064839051/362467097) (23316386/17161,112587711527/2248091) (24006368/466489,113239660853/318611987) (25012736/931225,87178804859/898632125) (34033612/700569,189719944165/586376253) (29326727/808201,141283390696/726572699) 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(13989283941350583497/9468047398347664,52322990355939958995841109125/921277861499702076308288) (18165439127822034359/789200480464810969,33091910545106978460935207224/701101685949914157408136547) (27941381672893842457/972344540657403684,112479712919745370493711824925/958804956023691429384286248) (80716163972678530603/7540890867919809,725171569434413166919370935978/654838166078353353644127) (67374721574751613559/2226686228363169049,442492876573694296693290173464/3322680132383265540396899843) (508793829613463972278/19198979522819264169,7821635860433452276710596988593/84123477661461082112447650197) (751181728873555075721/6765817555086990400,20513054177742456169623630685019/17598693345477890940502208000) (759008704631244321889/25897047633183356100,16252793165968186738105910414287/131787853179612695729113059000) (937499483032091385017/30364827786082716004,23343661327012081840940458985395/167323227673165650239371148008) 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