% Please read the comments on the pdf version. % The format of these examples is the following: each % example is given as a list with four elements. % The first one are the curve coefficients, in the % usual form [a_1,a_2,a_3,a_4,a_6]. The second one is the % list given by the permutation involved [sigma(0),..., % sigma(5)]. The third element is the list [a,d,b,d'] and % the fourth element is the rank of the curve or the upper % found by APECS. % % We would be very happy to know comments and/or new addtions % to the list. [[180,-8100,0,-4892251392,134063884477440],[3,2,1,4,5,0],[66432,-20304,13044672,-5725728],5] [[180,-8100,0,-4892251392,134063884477440],[0,5,4,1,2,3],[-35088,20304,-13044672,5725728],5] [[20,-100,0,-36478512,82321246080],[4,2,3,1,5,0],[5724,-1584,-367704,139392],5] [[-60,-900,0,-86832,8864640],[5,3,4,2,0,1],[-324,144,9288,-3456],2] [[-20,-100,0,-466992,549797760],[0,4,5,3,1,2],[1308,-432,-33576,3456],3] [[-2,-1,0,-238707,41709006],[1,5,0,4,2,3],[-513,180,8487,-3600],3] [[-180,-8100,0,-51432192,368371860480],[0,3,4,5,2,1],[-9312,4752,-638496,313632],4] [[-612,-93636,0,-26962612992,1882111797863424],[1,4,5,0,3,2],[-164832,66960,-19904832,12454560],5] [[396,-39204,0,-388106595072,88686989876929536],[2,5,0,1,4,3],[-715488,235440,459510624,-153977760],5] [[-576,-82944,0,-271059091200,49072046238950400],[1,3,4,5,0,2],[734160,-265680,-415035360,130714560],5] [[-576,-82944,0,-271059091200,49072046238950400],[3,5,0,1,2,4],[-594240,265680,238537440,-130714560],5] [[396,-39204,0,-388106595072,88686989876929536],[3,0,5,4,1,2],[-715488,235440,-310378176,153977760],5] [[-612,-93636,0,-26962612992,1882111797863424],[4,1,0,5,2,3],[-164832,66960,42367968,-12454560],5] [[-180,-8100,0,-51432192,368371860480],[5,2,1,0,3,4],[-9312,4752,929664,-313632],4] [[-300,-22500,0,-894074112,19561912750080],[2,3,0,1,4,5],[-30384,11808,-6045408,2904768],6] [[-60,-900,0,-48045312,189087436800],[3,4,1,2,5,0],[-7344,3744,-714528,292032],5] [[-60,-900,0,-48045312,189087436800],[5,0,3,4,1,2],[11376,-3744,745632,-292032],5] [[300,-22500,0,-894074112,19561912750080],[0,1,4,5,2,3],[28656,-11808,-8478432,2904768],6] [[-1800,-810000,0,-7410269014272,8108956611489899520],[3,0,2,1,4,5],[2763696,-577584,3502719072,-1323822528],6] [[2880,-2073600,0,-403246536682752,3207719147336296058880],[4,1,3,2,5,0],[-829968,5312736,62302243392,-30155089536],6] [[4680,-5475600,0,-3994541989632,6207305561351930880],[5,2,4,3,0,1],[-2327712,728784,-3390388704,2107643328],7] [[-2880,-2073600,0,-8792422324992,14409886139859502080],[0,3,5,4,1,2],[7563792,-2228688,-8618074272,1791865152],11] [[7632,-14561856,0,,-1208964238739712,23944945010158503235584],[1,4,0,5,2,3],[-42040752,12290400,265952884032,-83918851200],7] [[-6912,-11943936,0,-214026269587200,1973672371225801958400],[2,5,0,1,3,4],[-9752640,7294320,76016037600,-26872274880],8] [[120,-3600,0,-81948672,327577374720],[5,3,2,1,4,0],[8064,-3168,1169856,-418176],4] [[960,-230400,0,-92277352334592,342160070800370356224],[0,4,3,2,5,1],[11544048,-3013920,-34095021120,10813944960],4] [[2616,-1710864,0,-3327107104512,3360005144504534016],[1,5,4,3,0,2],[-515808,403920,-2454087456,906396480],6] [[-3072,-2359296,0,-2328753038487552,49786655684722942869504],[2,0,5,4,1,3],[-55130112,19313280,240362650368,-111012733440],6] [[-4944,-6110784,-14552162687232,21391150302252205056],[3,1,0,5,2,4],[1164672,340560,5468006304,-44953920],7] [[-960,-230400,0,-19321742592,1033886822584320],[4,2,1,0,3,5],[60912,6048,38636352,-72576],5] [[40,-400,0,-8854272,8259978240],[1,5,3,4,2,0],[-2448,1584,242208,-69696],4] [[-64,-1024,0,-1389312,394896384],[2,0,4,5,3,1],[-1152,720,-44064,14400],3] [[-64,-1024,0,-1389312,394896384],[4,2,0,1,5,3],[2448,-720,27936,-14400],3] [[-40,-400,0,-8854272,8259978240],[5,3,1,2,0,4],[5472,-1584,106272,-69696],4] [[-1080,-291600,-4379037151491072,136063103467431710822400],[2,4,0,3,1,5],[-77988192,33054048,-438167226816,226486336896],8] [[-720,-129600,0,-9969629720832,13778174775900128256],[3,5,1,4,2,0],[-3640128,1648080,-6422790240,2155688640],1] [[5544,-7683984,0,-422337203926272,3401406251614088487936],[4,0,2,5,3,1],[-18956688,10568880,102961496736,-29550588480],7] [[1080,-291600,0,-4379037151491072,136063103467431710822400],[5,1,3,0,4,2],[87282048,-33054048,438167226816,-226486336896],8] [[-720,-129600,0,-9969629720832,13778174775900128256],[0,2,4,1,5,3],[4600272,-1648080,-6422790240,2155688640],1] [[-5544,-7683984,0,-422337203926272,3401406251614088487936],[1,3,5,2,0,4],[33887712,-10568880,-102961496736,29550588480],7] [[20,-100,0,-466992,549797760],[3,4,2,0,1,5],[-852,432,16296,3456],3] [[-60,-900,0,-86832,8864640],[4,5,3,1,2,0],[396,-144,-7992,3456],2] [[-20,-100,0,-36478512,82321246080],[5,0,4,2,3,1],[-2196,1584,-329256,139392],5] [[-4,-4,0,-3819312,2669376384],[2,3,1,5,0,4],[1548,-720,-76104,28800],3] [[-2880,-2073600,0,-110993807215872,445121432212494274560],[4,0,2,3,1,5],[14071152,-3627936,35652163392,-14061879936],7] [[360,-32400,0,-27909792000,1526822144640000],[5,1,3,4,2,0],[-99600,75600,73720800,-22680000],5] [[-7056,-12446784,0,-129437671756032,543091962160151110656],[1,3,5,0,4,2],[17527152,-4944240,-5119105824,6467065920],5] [[-7488,-14017536,0,-841545692773632,15278101189303210758144],[2,4,0,1,5,3],[-34464912,10864800,-202374030528,65579932800],8] [[-6696,-11209104,0,-1767944739520512,27067552170879621206016],[3,5,1,2,0,4],[-46912128,22001760,291906110016,-122241778560],7] [[-90,-2025,0,-3434834187,7407635019590],[0,5,3,4,2,1],[39747,-2376,3706047,-627264],5] [[306,-23409,0,-338359707,3186238861494],[1,0,4,5,3,2],[-21237,11880,3783861,-1425600],4] [[-612,-93636,0,-5413755312,203919287135616],[3,2,0,1,5,4],[152652,-47520,26753112,-11404800],4] [[-90,-2025,0,-3434834187,77407635019590],[4,3,1,2,0,5],[27867,2376,569727,627264],5] [[396,-39204,0,-388106595072,88686989876929536],[2,1,4,5,0,3],[461712,-235440,-310378176,153977760],5] [[-612,-93636,0,-26962612992,1882111797863424],[3,2,5,0,1,4],[169968,-66960,42367968,-12454560],5] [[-180,-8100,0,-51432192,368371860480],[4,3,0,1,2,5],[14448,-4752,929664,-313632],4] [[-48,-576,0,-9262512,8383430016],[2,5,0,3,4,1],[-3348,1440,-123552,43200],2] [[-24,-144,0,-578907,130991094],[4,1,2,5,0,3],[963,-360,11556,-5400],2] [[-60,-900,0,-767232,253808640],[5,2,3,0,1,4],[1008,-288,16416,-1728],3] [[-60,-900,0,-767232,253808640],[1,4,5,2,3,0],[-432,288,7776,1728],3] [[-5184,-6718464,0,-142783615579392,708085096419827994624],[3,5,2,0,4,1],[13189008,-5387040,-40963299264,13898563200],4] [[-2142,-1147041,0,-15808640228307,39293749322977053294],[4,0,3,1,5,2],[5885823,-1961820,10341141993,-4072738320],7] [[-612,-93636,0,-52888734000,42522157354464000],[5,1,4,2,0,3],[-243780,110160,98574840,-44945280],5] [[-396,-39204,-16655166000,690091901769600],[0,2,5,3,1,4],[250140,-71280,-60813720,18817920],4] [[-1710,-731025,0,-1041760268307,785868626594613294],[1,3,0,4,2,5],[-1270977,427140,-1427543055,579201840],5] [[-3240,-2624400,0,-2359518446592,1392039372309073920],[2,4,1,5,3,0],[502176,175392,1361800512,14732928],7] [[-60,-900,0,-48045312,189087436800],[5,0,3,4,1,2],[11376,-3744,745632,-292032],5] [[300,-22500,0,-894074112,19561912750080],[0,1,4,5,2,3],[28656,-11808,-8478432,2904768],6] [[-300,-22500,0,-894074112,19561912750080],[2,3,0,1,4,5],[-30384,11808,-6045408,2904768],6] [[-60,-900,0,-48045312,189087436800],[3,4,1,2,5,0],[-7344,3744,-714528,292032],5] [[-960,-230400,0,-13201887036672,17372103328571019264],[5,0,2,3,4,1],[5909328,-1703520,8039027520,-3454738560],6] [[600,-90000,0,-4185188352,119899753943040],[0,1,3,4,5,2],[52704,-12384,-22572864,6390144],7] [[768,-147456,0,-28465015272192,52273748736104702976],[1,2,4,5,0,3],[4297392,-2075760,-8562479328,3860913600],6] [[-4368,-4769856,0,-102164509274112,521183246173070966784],[2,3,5,0,1,4],[7567488,-3850560,20709101952,-8825483520],6] [[-192,-9216,0,-1067634432,20407326188544],[3,4,0,1,2,5],[-32832,12240,-6162912,2496960],4] [[120,-3600,0,-210573084672,33546735732363264],[4,5,1,2,3,0],[-495072,211680,-339888960,124467840],6] [[-180,-8100,0,-51432192,368371860480],[1,2,5,4,3,0],[14448,-4752,-638496,313632],4] [[-612,-93636,0,-26962612992,1882111797863424],[2,3,0,5,4,1],[169968,-66960,-19904832,12454560],5] [[396,-39204,0,-388106595072,88686989876929536],[3,4,1,0,5,2],[461712,-235440,459510624,-153977760],5] [[-60,-900,0,-48045312,189087436800],[2,1,4,3,0,5],[-7344,3744,745632,-292032],5] [[-300,-22500,0,-894074112,19561912750080],[3,2,5,4,1,0],[-30384,11808,8478432,-2904768],6] [[300,-22500,0,-894074112,19561912750080],[5,4,1,0,3,2],[28656,-11808,6045408,-2904768],6] [[-60,-900,0,-48045312,189087436800],[0,5,2,1,4,3],[11376,-3744,-714528,292032],5] [[-3240,-2624400,0,-2359518446592,1392039372309073920],[3,1,4,0,2,5],[502176,175392,1435465152,-14732928],7] [[-1710,-731025,0,-1041760268307,785868626594613294],[4,2,5,1,3,0],[-1270977,427140,1468466145,-579201840],5] [[-396,-39204,0,-16655166000,690091901769600],[5,3,0,2,4,1],[250140,-71280,33275880,-18817920],4] [[-612,-93636,0,-52888734000,4252215735446400],[0,4,1,3,5,2],[-243780,110160,-126151560,44945280],5] [[4284,-4588164,0,-252938243652912,2514799956670531410816],[1,5,2,4,0,3],[23543292,-7847280,80180396856,-32581906560],7] [[-5184,-6718464,0,-142783615579392,708085096419827994624],[2,0,3,5,1,4],[13189008,-5387040,28529516736,-13898563200],4] [[-60,-900,0,-767232,253808640],[4,1,0,3,2,5],[-432,288,16416,-1728],3] [[-60,-900,0,-767232,253808640],[0,3,2,5,4,1],[1008,-288,7776,1728],3] [[-24,-144,0,-578907,130991094],[1,4,3,0,5,2],[963,-360,-15444,5400],2] [[-48,-576,0,-9262512,8383430016],[3,0,5,2,1,4],[-3348,1440,92448,-43200],2] [[120,-3600,0,-81948672,327577374720],[5,1,4,3,2,0],[-7776,3168,-921024,418176],4] [[-960,-230400,0,-19321742592,1033886822584320],[0,2,5,4,3,1],[91152,-6048,38273472,72576],5] [[-4944,-6110784,0,-14552162687232,21391150302252205056],[1,3,0,5,4,2],[2867472,-340560,5243236704,44953920],7] [[-3072,-2359296,0,-2328753038487552,49786655684722942869504],[2,4,1,0,5,3],[41436288,-19313280,-314701016832,111012733440],6] [[-2616,-1710864,0,-3327107104512,3360005144504534016],[3,5,2,1,0,4],[1503792,-403920,-2077894944,906396480],6] [[-960,-230400,0,-92277352334592,342160070800370356224],[4,0,3,2,1,5],[-3525552,3013920,-19974703680,10813944960],4] [[-60,-900,0,-767232,253808640],[1,4,5,2,3,0],[-432,288,7776,1728],3]