History of $j$-invariants of elliptic curves over $\mathbb{Q}$ with good reduction outside $\{2, 3, 5\}$

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2026-08-09 09:14 flattening entries rewritten as records with named parameters current
2026-08-09 08:35 data-repository import the current state of the data repository reviewed
2021-05-07 17:53 admin from the data repository, 42a87287
2021-05-06 21:00 admin from the data repository, cfa26fe2

The first version, 2021-05-06 21:00

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+Title: $j$-invariants of elliptic curves over $\mathbb{Q}$ with  good reduction outside+  $\{2, 3, 5\}$+Definition: This table contains the $j$-invariants of all  elliptic curves $\mathbb{Q}$+  with good reduction outside $\{2,3,5\}$.+Parameters: ''+Comments:+  comment-minimal-discriminant-and-N: An elliptic curve $E/\mathbb{Q}$ has good reduction+    at a prime $p$ if and only if $p$ does not divide the minimal discriminant of+    $E$,  and equivalently, if and only if $p$ does not divide the conductor of $E$.+Formulas: {}+Programs: {}+References: {}+Links:+  SUE:+    title: Tables of elliptic curves with good reduction away from the first primes+    url: https://github.com/bmatschke/s-unit-equations/tree/master/elliptic-curve-tables/good-reduction-away-from-first-primes+  Wiki:+    title: 'Wikipedia: j-invariant'+    url: https://en.wikipedia.org/wiki/J-invariant+Similar tables: ''+Keywords: ''+Tags:+- number theory+- ellptic curves+Data properties:+  type: Q+  complete: 'yes'+  sources:+  - CITE{SUE}+Display properties:+  number-header: $j$+Numbers:+- '0'+- '-6'+- -9/5+- -1/15+- -24/5+- -25/2+- -18/25+- '-36'+- -64/25+- 64/9+- 64/3+- '-72'+- -72/5+- 81/2+- -108/5+- '108'+- -128/9+- '128'+- 135/8+- '160'+- '-192'+- '192'+- '-216'+- '270'+- '288'+- '-300'+- '-320'+- '405'+- '-432'+- '432'+- '-450'+- -486/5+- '-576'+- -576/5+- '576'+- '648'+- -768/5+- '768'+- '-864'+- 864/25+- 864/5+- '864'+- '960'+- '-972'+- -243/1000+- '1080'+- '-1152'+- '1152'+- '1296'+- '1440'+- '1458'+- '1536'+- '1600'+- '1620'+- '-1728'+- -1728/5+- 1728/25+- 1728/5+- '1728'+- '-1800'+- '1800'+- '1875'+- '1920'+- -1944/5+- '1944'+- 2048/3+- '2048'+- '-2160'+- '2160'+- -2187/25+- '2304'+- -2560/3+- '-2592'+- '2592'+- '2700'+- '-2880'+- '2880'+- '-3072'+- 3375/2+- '-3456'+- -3456/25+- 3456/5+- '3456'+- 3645/4+- '3888'+- 4000/9+- '4320'+- '4374'+- '4608'+- '4800'+- '-5000'+- 5120/3+- '-5184'+- -5184/5+- -5184/125+- 5184/5+- '5184'+- 5488/81+- '-6075'+- 6561/32+- '-6912'+- -6912/5+- 6912/125+- 6912/5+- '6912'+- '-7680'+- 7776/3125+- 7776/5+- -8000/81+- '8000'+- '-8640'+- '8640'+- 8748/5+- 9216/5+- 9261/8+- 10125/64+- 10368/5+- '10368'+- '10976'+- '11250'+- -12288/25+- 12800/27+- '-13824'+- 13824/5+- '-15552'+- 15552/25+- 15552/5+- '15552'+- 16000/3+- 16384/5+- '17280'+- -17496/5+- '-18522'+- '-19440'+- -19683/10+- 20480/243+- 21296/25+- 21296/15+- '-21600'+- 21952/75+- 21952/9+- '23328'+- -24389/12+- '-25920'+- 27436/27+- 27648/25+- '27648'+- 27783/16+- '-30720'+- '-32928'+- 35152/9+- -35937/4+- 36864/5+- -40960/27+- '-41472'+- -41472/25+- 41472/25+- 42592/9+- '43200'+- 43904/45+- 43904/3+- 46305/2+- -46656/5+- 46656/125+- 46656/25+- '54000'+- 55296/5+- 59319/40+- 69984/125+- '-72000'+- '73728'+- '78608'+- '-82944'+- 85184/5625+- 85184/405+- 85184/3+- '86400'+- 93312/5+- 97336/81+- -102400/3+- 107811/8+- 109503/64+- -121945/32+- 131072/9+- -132651/2+- '-138240'+- -138915/4096+- '139968'+- 140608/81+- 140608/3+- -140625/8+- -148176/5+- 148176/25+- 157464/25+- -165888/25+- 165888/625+- 177147/5+- 177957/250+- 191664/125+- 195112/9+- 197568/125+- '-207360'+- 207646/6561+- '-209952'+- -219488/729+- 219488/75+- -219501/2048+- 221184/125+- 237276/625+- -248832/25+- 281216/225+- '287496'+- 296595/64+- 308655/512+- 314432/75+- 314432/45+- '-316368'+- 357911/2160+- -373248/625+- 389344/3+- '419904'+- 421824/78125+- -314432/421875+- 438976/225+- 438976/5+- 444528/125+- -446631/128+- 470596/225+- '-474552'+- '-497664'+- 555579/2+- -592704/625+- -592704/3125+- 592704/5+- '-622080'+- -628864/3645+- 778688/45+- '790272'+- 804357/500+- 839808/125+- 884736/5+- 898425/512+- 953312/405+- 995328/625+- '1000188'+- 1022208/3125+- -1058841/250+- 1073733/1000+- 1097505/8+- 1149984/625+- '-1166400'+- -1167051/512+- 1193859/512+- '1200000'+- -1339893/4+- '1463340'+- 1556068/81+- -1557376/625+- 1601613/163840+- -1642545/8+- '-1658880'+- 1778112/5+- -1860867/320+- 1898208/5+- 1906624/225+- -1975392/5+- -1975392/625+- 2060602/729+- -2146689/2000+- '-2194880'+- 2359296/125+- -2654208/15625+- 2744000/9+- -2859936/125+- 2863288/1875+- 3241792/9+- 3316275/16+- -3472875/4+- 3631696/2025+- -3721734/3125+- 3721734/25+- -3779136/125+- 4102893/2560+- '-4147200'+- -4244832/3125+- -5267712/125+- -5624320/177147+- -5659776/125+- -5971968/25+- -6440067/40+- 6483584/1265625+- 6644672/3645+- -6699465/2+- 6838155/4+- -6847995/64+- 7301384/3+- 43904/7381125+- -8120601/12800+- 8429568/15625+- -8780800/2187+- -9199872/5+- '-12288000'+- 2863288/13286025+- 13997521/225+- 14172488/1875+- 14526784/15+- 15166431/20480+- 15768432/5+- '16541040'+- 16747803/500+- 16979328/25+- -17173512/25+- 19056256/27+- -19465109/248832+- -20720464/15625+- '-21024576'+- 22639104/3125+- -24361803/1000+- 24897088/18225+- 24918016/45+- -27995042/1171875+- 28588707/320+- 28756228/3+- -29218112/6561+- -34167744/3125+- -36006768/625+- 36594368/16875+- 38614472/405+- -42144192/390625+- '-44789760'+- 46314747/3125+- 46969655/32768+- 48228544/2025+- 54607676/32805+- 57960603/31250+- '61740000'+- 62099136/25+- 62710839/125000+- 68450475/4096+- 92345408/675+- 94531131/8+- 96018048/3125+- 111284641/50625+- 111980168/32805+- 131872229/18+- 132304644/5+- 136835858/1875+- 164566592/46875+- -171307467/10+- -186297408/390625+- '214495200'+- -225866529/62500000+- 252179168/25+- -273359449/1536000+- 300605792/675+- 346478976/1953125+- -349938025/8+- 362225664/5+- 379297728/78125+- 409493637/250000+- -425920000/243+- 488095744/125+- 506024032/59049+- 546718898/405+- 702595369/72900+- -745936704/5+- '-784446336'+- 868327204/5625+- -873722816/59049+- 890277128/15+- -994121664/5+- -1159088625/2097152+- -1184303835/16+- 1541767203/512000+- -1568892672/78125+- 2156689088/81+- -2218426947/102400+- 2299120425/8+- '2472985728'+- '-2604751992'+- 3065617154/9+- 3229310592/125+- 4045602816/1953125+- 4543847424/3125+- 4733169839/3515625+- 6772724288/91125+- -7283146752/25+- 8144865728/1125+- -8302761792/25+- 8527173507/200+- 14784166784/243+- -15590912409/78125+- '15786448344'+- -16522921323/4000+- 20034997696/455625+- '-23203748160'+- 23937672968/45+- 24836849888/820125+- 26410345352/10546875+- -30866268160/3+- 35578826569/5314410+- -55011266559/8192+- 56667352321/15+- 58591911104/243+- 80273184813/262144000+- -87739741323/250000000+- -112584240576/78125+- -147281603041/215233605+- 183711891456/125+- -189613868625/128+- 192596360288/3796875+- 241750216332/48828125+- 272223782641/164025+- 290236765383/256+- '-325228538880'+- 502270291349/1889568+- 819699324507/80+- 1241603628992/597871125+- 1261112198464/675+- -1557792607653/67108864+- 1770025017602/75+- -1897537562112/390625+- 2656166199049/33750+- -2814932662848/3125+- -3809037964608/15625+- -3839138053504/87890625+- 4102915888729/9000000+- -4388755356576/48828125+- 10316097499609/5859375000+- 33940032554547/5368709120+- '-39091613782464'+- 44708635815488/34171875+- -99468145455264/125+- -115330920751809/4096000+- 499460194376672/253125+- 1114544804970241/405+- 3659668390116864/78125+- 13857745529076264/19073486328125+- 16778985534208729/81000+- 21782774971421163/128000+- -29372519473126518336/1953125+- -71697661607585576448/25 

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