Cremona's table of elliptic curves

68970 = 2 · 3 · 5 · 11² · 19

Class	r	Atkin-Lehner	Eigenvalues
68970a (2 curves)	1	2+ 3+ 5+ 11+ 19+	2+ 3+ 5+  2 11+ -2 -2 19+
Curve Equation t Generators 68970a1 [1,1,0,-2314248,-1272192192] 2 [13749:1595058:1] 68970a2 [1,1,0,-36387848,-84500367552] 2 [1684340357:178711977170:117649]
68970b (1 curve)	0	2+ 3+ 5+ 11- 19+	2+ 3+ 5+  0 11- -2 -3 19+
Curve Equation t 68970b1 [1,1,0,-1049591633,13264402599573] 1
68970c (4 curves)	0	2+ 3+ 5+ 11- 19+	2+ 3+ 5+  0 11- -2  6 19+
Curve Equation t 68970c1 [1,1,0,5322,-171948] 2 68970c2 [1,1,0,-33398,-1728492] 4 68970c3 [1,1,0,-193118,31205772] 2 68970c4 [1,1,0,-493198,-133507172] 2
68970d (1 curve)	0	2+ 3+ 5+ 11- 19+	2+ 3+ 5+  3 11-  1  3 19+
Curve Equation t 68970d1 [1,1,0,-331058,-73573452] 1
68970e (4 curves)	1	2+ 3+ 5+ 11- 19-	2+ 3+ 5+  0 11- -2 -2 19-
Curve Equation t Generators 68970e1 [1,1,0,-3753,-89547] 2 [-34:31:1] 68970e2 [1,1,0,-6173,36777] 4 [-44:497:1] 68970e3 [1,1,0,24077,321127] 2 [39:1130:1] 68970e4 [1,1,0,-75143,7885563] 2 [193:690:1]
68970f (1 curve)	1	2+ 3+ 5+ 11- 19-	2+ 3+ 5+ -1 11- -5  7 19-
Curve Equation t Generators 68970f1 [1,1,0,3452,44752] 1 [31:-443:1]
68970g (1 curve)	1	2+ 3+ 5+ 11- 19-	2+ 3+ 5+ -3 11- -1  1 19-
Curve Equation t Generators 68970g1 [1,1,0,-9013413,-10439850483] 1 [50871:11428002:1]
68970h (1 curve)	1	2+ 3+ 5+ 11- 19-	2+ 3+ 5+ -3 11- -1 -3 19-
Curve Equation t Generators 68970h1 [1,1,0,281202,1268553708] 1 [5979:462558:1]
68970i (2 curves)	0	2+ 3+ 5- 11+ 19+	2+ 3+ 5-  4 11+  6 -2 19+
Curve Equation t 68970i1 [1,1,0,-256962,50029236] 2 68970i2 [1,1,0,-254762,50930796] 2
68970j (1 curve)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5-  0 11-  0  4 19+
Curve Equation t Generators 68970j1 [1,1,0,103255348,-2776077721776] 1 [635235602759:529699048285388:912673]
68970k (1 curve)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5- -1 11-  1 -5 19+
Curve Equation t Generators 68970k1 [1,1,0,-99428727,381566704149] 1 [6285:67368:1]
68970l (2 curves)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5-  2 11-  6 -2 19+
Curve Equation t Generators 68970l1 [1,1,0,-444677,58713549] 2 [-502:12731:1] 68970l2 [1,1,0,1491323,434684749] 2 [103:24226:1]
68970m (2 curves)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5-  2 11- -6 -8 19+
Curve Equation t Generators 68970m1 [1,1,0,-2,3744] 2 [-5:63:1] 68970m2 [1,1,0,-3632,81426] 2 [7:234:1]
68970n (1 curve)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5-  4 11- -4  0 19+
Curve Equation t Generators 68970n1 [1,1,0,-76837,-8233331] 1 [11545:1234417:1]
68970o (4 curves)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5- -4 11-  6 -2 19+
Curve Equation t Generators 68970o1 [1,1,0,-229902,-44440524] 2 [9753526340:-674439168138:2048383] 68970o2 [1,1,0,-3724382,-2768038236] 4 [19048:2605406:1] 68970o3 [1,1,0,-3770362,-2696245064] 2 [2382:41764:1] 68970o4 [1,1,0,-59590082,-177080195376] 2 [480762725:61016441323:24389]
68970p (1 curve)	1	2+ 3+ 5- 11- 19+	2+ 3+ 5- -5 11-  1  3 19+
Curve Equation t Generators 68970p1 [1,1,0,-28007872,57237247456] 1 [2167:80929:1]
68970q (1 curve)	0	2+ 3+ 5- 11- 19-	2+ 3+ 5- -3 11-  3  1 19-
Curve Equation t 68970q1 [1,1,0,7582463,81276661] 1
68970r (2 curves)	0	2+ 3- 5+ 11+ 19+	2+ 3- 5+  2 11+ -2  6 19+
Curve Equation t 68970r1 [1,0,1,-1273154,-372352444] 2 68970r2 [1,0,1,-18460654,-30526102444] 2
68970s (2 curves)	1	2+ 3- 5+ 11+ 19-	2+ 3- 5+ -2 11+ -2  6 19-
Curve Equation t Generators 68970s1 [1,0,1,-3465564,-2483418038] 2 [-1075:771:1] 68970s2 [1,0,1,-3598664,-2282383798] 2 [-1305:14503:1]
68970t (2 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+  1 11-  1 -3 19+
Curve Equation t Generators 68970t1 [1,0,1,96,-794] 1 [8:18:1] 68970t2 [1,0,1,-894,25342] 1 [-14:194:1]
68970u (2 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+  2 11-  2 -2 19+
Curve Equation t Generators 68970u1 [1,0,1,-2940424,1686491222] 2 [169:34475:1] 68970u2 [1,0,1,4803576,9071169622] 2 [-694:73854:1]
68970v (2 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+  2 11-  2  4 19+
Curve Equation t Generators 68970v1 [1,0,1,-116889,-15497924] 2 [113039990:2662732039:148877] 68970v2 [1,0,1,-1873809,-987426068] 2 [7281686478933310:-130785342641658793:4224031292125]
68970w (2 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+ -2 11-  2  0 19+
Curve Equation t Generators 68970w1 [1,0,1,-113864,-103033438] 2 [7054:172161:8] 68970w2 [1,0,1,-4066934,-3142153654] 2 [26062:1065801:8]
68970x (4 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+ -2 11-  4  6 19+
Curve Equation t Generators 68970x1 [1,0,1,-3130394,-2151631924] 2 [1073628143247:-9100566958981:517781627] 68970x2 [1,0,1,-50213914,-136961166388] 2 [-1591978379:787233689:389017] 68970x3 [1,0,1,10344166,-11197986868] 2 [7258248970500139800505352124463:-167092613569467015275258439938085:7053116952414679215487414667] 68970x4 [1,0,1,-56050954,-103141949044] 2 [-29207084947874675:-238206647434298059:4671700873813]
68970y (2 curves)	1	2+ 3- 5+ 11- 19+	2+ 3- 5+ -2 11- -6 -4 19+
Curve Equation t Generators 68970y1 [1,0,1,-176179,28578746] 2 [109:-3322:1] 68970y2 [1,0,1,-2822449,1824866822] 2 [946:809:1]
68970z (1 curve)	0	2+ 3- 5+ 11- 19-	2+ 3- 5+  0 11-  0  0 19-
Curve Equation t 68970z1 [1,0,1,1672096,1505447876] 1
68970ba (1 curve)	0	2+ 3- 5+ 11- 19-	2+ 3- 5+  0 11- -6 -3 19-
Curve Equation t 68970ba1 [1,0,1,-11619,499486] 1
68970bb (2 curves)	0	2+ 3- 5+ 11- 19-	2+ 3- 5+  5 11- -1 -3 19-
Curve Equation t 68970bb1 [1,0,1,-80589,-9156314] 3 68970bb2 [1,0,1,-6598254,-6524214248] 1
68970bc (1 curve)	0	2+ 3- 5+ 11- 19-	2+ 3- 5+ -5 11- -5  5 19-
Curve Equation t 68970bc1 [1,0,1,-124,-43078] 1
68970bd (1 curve)	1	2+ 3- 5- 11- 19-	2+ 3- 5-  1 11- -1  5 19-
Curve Equation t Generators 68970bd1 [1,0,1,-1567558,-833411944] 1 [3640:-206008:1]
68970be (2 curves)	1	2+ 3- 5- 11- 19-	2+ 3- 5- -1 11- -1 -3 19-
Curve Equation t Generators 68970be1 [1,0,1,-26936418,128998573108] 3 [-6766:42405:1] 68970be2 [1,0,1,235104207,-2932474456892] 1 [591476:10731795:64]
68970bf (1 curve)	1	2+ 3- 5- 11- 19-	2+ 3- 5- -1 11-  3 -1 19-
Curve Equation t Generators 68970bf1 [1,0,1,-58,218] 1 [4:-10:1]
68970bg (4 curves)	1	2+ 3- 5- 11- 19-	2+ 3- 5-  2 11- -4  2 19-
Curve Equation t Generators 68970bg1 [1,0,1,1129532,982586306] 2 [385:-38593:1] 68970bg2 [1,0,1,-10641348,11510461378] 2 [3809:-163905:1] 68970bg3 [1,0,1,-399477268,3073135105346] 2 [11517:-1481:1] 68970bg4 [1,0,1,-6391636848,196682207998978] 2 [46067:-56793:1]
68970bh (4 curves)	1	2+ 3- 5- 11- 19-	2+ 3- 5-  2 11-  6  2 19-
Curve Equation t Generators 68970bh1 [1,0,1,-3300278,-2666132152] 2 [3024:121000:1] 68970bh2 [1,0,1,-55049558,-157210181944] 2 [-4290:3997:1] 68970bh3 [1,0,1,-7765178,217889386328] 2 [-628:472032:1] 68970bh4 [1,0,1,-592380308,5494391703656] 2 [236834542:-14197477272:12167]
68970bi (4 curves)	1	2+ 3- 5- 11- 19-	2+ 3- 5- -4 11-  2  2 19-
Curve Equation t Generators 68970bi1 [1,0,1,-1213,-27832] 2 [87:682:1] 68970bi2 [1,0,1,-22993,-1343344] 4 [186:814:1] 68970bi3 [1,0,1,-26623,-891772] 2 [-36:160:1] 68970bi4 [1,0,1,-367843,-85900564] 2 [6456:513139:1]
68970bj (2 curves)	1	2- 3+ 5+ 11+ 19-	2- 3+ 5+ -2 11+  2  2 19-
Curve Equation t Generators 68970bj1 [1,1,1,-19126,947123] 2 [17:783:1] 68970bj2 [1,1,1,-300726,63349683] 2 [337:-817:1]
68970bk (2 curves)	1	2- 3+ 5+ 11- 19+	2- 3+ 5+  0 11- -2 -4 19+
Curve Equation t Generators 68970bk1 [1,1,1,22564,-18730051] 2 [281:3005:1] 68970bk2 [1,1,1,-935756,-337658947] 2 [-489:2059:1]
68970bl (1 curve)	1	2- 3+ 5+ 11- 19+	2- 3+ 5+  1 11-  5 -7 19+
Curve Equation t Generators 68970bl1 [1,1,1,417629,-57476671] 1 [1139:42990:1]
68970bm (2 curves)	1	2- 3+ 5+ 11- 19+	2- 3+ 5+  2 11-  6 -4 19+
Curve Equation t Generators 68970bm1 [1,1,1,-9501,1246323] 2 [39:-988:1] 68970bm2 [1,1,1,-241821,45572979] 2 [-321:9660:1]
68970bn (1 curve)	1	2- 3+ 5+ 11- 19+	2- 3+ 5+  3 11-  1 -1 19+
Curve Equation t Generators 68970bn1 [1,1,1,-1090623036,13889987877789] 1 [19789:230105:1]
68970bo (1 curve)	1	2- 3+ 5+ 11- 19+	2- 3+ 5+  3 11-  1  3 19+
Curve Equation t Generators 68970bo1 [1,1,1,2324,-952027] 1 [671:17079:1]
68970bp (1 curve)	0	2- 3+ 5+ 11- 19-	2- 3+ 5+  0 11-  2  3 19-
Curve Equation t 68970bp1 [1,1,1,-8674311,-9969684867] 1
68970bq (2 curves)	0	2- 3+ 5+ 11- 19-	2- 3+ 5+ -2 11-  0 -2 19-
Curve Equation t 68970bq1 [1,1,1,-11921,-554641] 2 68970bq2 [1,1,1,-195841,-33439537] 2
68970br (1 curve)	2	2- 3+ 5+ 11- 19-	2- 3+ 5+ -3 11- -1 -3 19-
Curve Equation t Generators 68970br1 [1,1,1,-2736,54033] 1 [21:-91:1]&[-11:293:1]
68970bs (2 curves)	0	2- 3+ 5- 11+ 19-	2- 3+ 5- -4 11+ -6  2 19-
Curve Equation t 68970bs1 [1,1,1,-31092465,-66744375345] 2 68970bs2 [1,1,1,-30826265,-67943020705] 2
68970bt (4 curves)	0	2- 3+ 5- 11- 19+	2- 3+ 5-  0 11-  6  2 19+
Curve Equation t 68970bt1 [1,1,1,-8775,147885] 4 68970bt2 [1,1,1,-69275,-6942715] 4 68970bt3 [1,1,1,-2725,-19640455] 2 68970bt4 [1,1,1,-1103825,-446833375] 2
68970bu (2 curves)	0	2- 3+ 5- 11- 19+	2- 3+ 5-  2 11-  0  2 19+
Curve Equation t 68970bu1 [1,1,1,-2120,-102343] 2 68970bu2 [1,1,1,-48100,-4075015] 2
68970bv (1 curve)	0	2- 3+ 5- 11- 19+	2- 3+ 5-  3 11- -3 -1 19+
Curve Equation t 68970bv1 [1,1,1,917477960,-103591845895] 1
68970bw (1 curve)	1	2- 3+ 5- 11- 19-	2- 3+ 5-  0 11-  0 -4 19-
Curve Equation t Generators 68970bw1 [1,1,1,853350,2086096167] 1 [3337:203531:1]
68970bx (1 curve)	1	2- 3+ 5- 11- 19-	2- 3+ 5-  1 11- -1  5 19-
Curve Equation t Generators 68970bx1 [1,1,1,-12030876030,-507925437602373] 1 [127501:5492039:1]
68970by (2 curves)	1	2- 3+ 5- 11- 19-	2- 3+ 5-  2 11-  2 -6 19-
Curve Equation t Generators 68970by1 [1,1,1,3325,-190915] 2 [334:1039:8] 68970by2 [1,1,1,-36605,-2411023] 2 [23566:1264763:8]
68970bz (2 curves)	1	2- 3+ 5- 11- 19-	2- 3+ 5- -2 11-  2  2 19-
Curve Equation t Generators 68970bz1 [1,1,1,-333660,-67420935] 2 [-407:1283:1] 68970bz2 [1,1,1,422590,-328175935] 2 [206254:33025459:8]
68970ca (2 curves)	1	2- 3+ 5- 11- 19-	2- 3+ 5- -2 11-  2  2 19-
Curve Equation t Generators 68970ca1 [1,1,1,-174370380,887662459245] 2 [-3635:1215689:1] 68970ca2 [1,1,1,-2791222860,56758509648237] 2 [30477:-7639:1]
68970cb (4 curves)	1	2- 3+ 5- 11- 19-	2- 3+ 5- -4 11- -2  6 19-
Curve Equation t Generators 68970cb1 [1,1,1,-807375,-313765803] 2 [10190:210523:8] 68970cb2 [1,1,1,-13352655,-18785436075] 4 [100302:10637775:8] 68970cb3 [1,1,1,-13788255,-17494840395] 2 [5539:273110:1] 68970cb4 [1,1,1,-213641535,-1202012023563] 2 [-210112567404:105047816283:24897088]
68970cc (1 curve)	1	2- 3+ 5- 11- 19-	2- 3+ 5- -4 11-  4  0 19-
Curve Equation t Generators 68970cc1 [1,1,1,-635,5897] 1 [15:-14:1]
68970cd (1 curve)	1	2- 3+ 5- 11- 19-	2- 3+ 5-  5 11- -1 -3 19-
Curve Equation t Generators 68970cd1 [1,1,1,-231470,-43108405] 1 [4773:325663:1]
68970ce (2 curves)	1	2- 3- 5+ 11+ 19+	2- 3- 5+  2 11+  2 -6 19+
Curve Equation t Generators 68970ce1 [1,0,0,-28641,1863225] 2 [-12:1491:1] 68970ce2 [1,0,0,-29741,1712085] 2 [-14:1465:1]
68970cf (2 curves)	0	2- 3- 5+ 11+ 19-	2- 3- 5+ -2 11+  2 -6 19-
Curve Equation t 68970cf1 [1,0,0,-154051576,495447051056] 2 68970cf2 [1,0,0,-2233739076,40628008613556] 2
68970cg (1 curve)	0	2- 3- 5+ 11- 19+	2- 3- 5+  0 11-  0  0 19+
Curve Equation t 68970cg1 [1,0,0,13819,-1129809] 1
68970ch (2 curves)	0	2- 3- 5+ 11- 19+	2- 3- 5+  0 11-  6  0 19+
Curve Equation t 68970ch1 [1,0,0,2719654,-964015260] 2 68970ch2 [1,0,0,-12613466,-8265647004] 2
68970ci (1 curve)	0	2- 3- 5+ 11- 19+	2- 3- 5+  0 11-  6  3 19+
Curve Equation t 68970ci1 [1,0,0,-96,-384] 1
68970cj (4 curves)	0	2- 3- 5+ 11- 19+	2- 3- 5+  0 11- -6 -6 19+
Curve Equation t 68970cj1 [1,0,0,-53666,6193716] 2 68970cj2 [1,0,0,-927286,343585760] 4 68970cj3 [1,0,0,-996256,289499486] 2 68970cj4 [1,0,0,-14836236,21994257330] 2
68970ck (2 curves)	0	2- 3- 5+ 11- 19+	2- 3- 5+  2 11- -2 -2 19+
Curve Equation t 68970ck1 [1,0,0,-31043581,-66620103439] 2 68970ck2 [1,0,0,-496787101,-4261944582895] 2
68970cl (4 curves)	0	2- 3- 5+ 11- 19+	2- 3- 5+ -2 11- -2  6 19+
Curve Equation t 68970cl1 [1,0,0,62494,3674496] 2 68970cl2 [1,0,0,-296876,31777230] 2 68970cl3 [1,0,0,-1282421,567690465] 2 68970cl4 [1,0,0,-20608541,36007929321] 2
68970cm (1 curve)	0	2- 3- 5+ 11- 19+	2- 3- 5+  5 11-  5 -5 19+
Curve Equation t 68970cm1 [1,0,0,-14946,57321540] 1
68970cn (2 curves)	0	2- 3- 5+ 11- 19+	2- 3- 5+ -5 11-  1  3 19+
Curve Equation t 68970cn1 [1,0,0,-9751211,12177302391] 1 68970cn2 [1,0,0,-798388676,8682930775080] 1
68970co (2 curves)	1	2- 3- 5+ 11- 19-	2- 3- 5+ -1 11- -1  3 19-
Curve Equation t Generators 68970co1 [1,0,0,11674,1068156] 3 [-162:7341:8] 68970co2 [1,0,0,-108116,-33838650] 1 [34974:2288013:8]
68970cp (2 curves)	1	2- 3- 5+ 11- 19-	2- 3- 5+  2 11- -2  2 19-
Curve Equation t Generators 68970cp1 [1,0,0,-5113281,4448484261] 2 [-762:89277:1] 68970cp2 [1,0,0,-4357031,5810188011] 2 [17438:644681:8]
68970cq (4 curves)	1	2- 3- 5+ 11- 19-	2- 3- 5+ -4 11- -2  2 19-
Curve Equation t Generators 68970cq1 [1,0,0,444854,685448996] 2 [308:-29338:1] 68970cq2 [1,0,0,-9467466,10619576100] 4 [3156:-111930:1] 68970cq3 [1,0,0,-28285386,-44708872284] 2 [6720:258726:1] 68970cq4 [1,0,0,-149246666,701771808420] 2 [7336:-45050:1]
68970cr (2 curves)	1	2- 3- 5- 11- 19+	2- 3- 5-  1 11-  1  3 19+
Curve Equation t Generators 68970cr1 [1,0,0,-222615,-96938775] 1 [1830:74085:1] 68970cr2 [1,0,0,1943010,2203388100] 1 [1500:-92910:1]
68970cs (1 curve)	1	2- 3- 5- 11- 19+	2- 3- 5-  1 11- -3  1 19+
Curve Equation t Generators 68970cs1 [1,0,0,-6960,-297450] 1 [13140:162015:64]
68970ct (1 curve)	1	2- 3- 5- 11- 19+	2- 3- 5- -1 11-  1 -5 19+
Curve Equation t Generators 68970ct1 [1,0,0,-12955,624977] 1 [74:233:1]
68970cu (4 curves)	1	2- 3- 5- 11- 19+	2- 3- 5- -2 11- -2  0 19+
Curve Equation t Generators 68970cu1 [1,0,0,-2725,-676543] 2 [494:-11137:1] 68970cu2 [1,0,0,-133405,-18631975] 2 [-220:395:1] 68970cu3 [1,0,0,24500,18157712] 2 [32:4340:1] 68970cu4 [1,0,0,-904780,319802000] 2 [736:6892:1]
68970cv (8 curves)	1	2- 3- 5- 11- 19+	2- 3- 5-  4 11- -2 -6 19+
Curve Equation t Generators 68970cv1 [1,0,0,-10467410,-11440172028] 4 [-2366:10258:1] 68970cv2 [1,0,0,-161717410,-791557422028] 4 [-7366:5258:1] 68970cv3 [1,0,0,-211251785,1180299491097] 4 [-15566:842683:1] 68970cv4 [1,0,0,-155969910,-850424466528] 2 [15624:717948:1] 68970cv5 [1,0,0,-2587464910,-50659589377528] 2 [505724:357494528:1] 68970cv6 [1,0,0,-273203785,431436105497] 4 [-16078:825275:1] 68970cv7 [1,0,0,1054698615,3395048681817] 2 [-108980874:-156948299451:103823] 68970cv8 [1,0,0,-2592338185,-50459185341223] 2 [638840160845002:-452229551068554317:1263214441]
68970cw (4 curves)	0	2- 3- 5- 11- 19-	2- 3- 5-  4 11-  6  6 19-
Curve Equation t 68970cw1 [1,0,0,1510,19812] 2 68970cw2 [1,0,0,-8170,180500] 4 68970cw3 [1,0,0,-54150,-4720968] 2 68970cw4 [1,0,0,-117070,15404720] 2

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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