Cremona's table of elliptic curves

61050 = 2 · 3 · 5² · 11 · 37

Class	r	Atkin-Lehner	Eigenvalues
61050a (2 curves)	1	2+ 3+ 5+ 11+ 37+	2+ 3+ 5+  1 11+  7  3 -4
Curve Equation t Generators 61050a1 [1,1,0,-13900,625000] 1 [65:5:1] 61050a2 [1,1,0,-23650,-371750] 1 [-145:260:1]
61050b (1 curve)	1	2+ 3+ 5+ 11+ 37+	2+ 3+ 5+ -1 11+ -1  7 -8
Curve Equation t Generators 61050b1 [1,1,0,-12375,-232875] 1 [-85:505:1]
61050c (1 curve)	1	2+ 3+ 5+ 11+ 37+	2+ 3+ 5+  2 11+  0  0 -1
Curve Equation t Generators 61050c1 [1,1,0,22800,-576000] 1 [96:-1632:1]
61050d (2 curves)	1	2+ 3+ 5+ 11+ 37+	2+ 3+ 5+  4 11+ -5  6 -1
Curve Equation t Generators 61050d1 [1,1,0,1232800,-2376576000] 1 [462804484541:15974384083895:313046839] 61050d2 [1,1,0,-104067200,-408907476000] 1 [246799895519862742158573008281241:107702713060430780569832890058460395:1289227089376255146526716139]
61050e (2 curves)	1	2+ 3+ 5+ 11+ 37+	2+ 3+ 5+ -4 11+ -4 -2 -2
Curve Equation t Generators 61050e1 [1,1,0,-1514575,336041125] 2 [18070:1361077:125] 61050e2 [1,1,0,-20458575,35590825125] 2 [2190:34905:1]
61050f (1 curve)	0	2+ 3+ 5+ 11+ 37-	2+ 3+ 5+  4 11+  5  7 -6
Curve Equation t 61050f1 [1,1,0,-849700,294274000] 1
61050g (1 curve)	0	2+ 3+ 5+ 11- 37+	2+ 3+ 5+  0 11-  7  3  6
Curve Equation t 61050g1 [1,1,0,-2200,30250] 1
61050h (2 curves)	0	2+ 3+ 5+ 11- 37+	2+ 3+ 5+ -3 11-  1 -3  0
Curve Equation t 61050h1 [1,1,0,-3272250,-2127487500] 1 61050h2 [1,1,0,-2006961000,-34607243426250] 1
61050i (4 curves)	0	2+ 3+ 5+ 11- 37+	2+ 3+ 5+  4 11-  4  6  2
Curve Equation t 61050i1 [1,1,0,-38450,1048500] 2 61050i2 [1,1,0,-334450,-73839500] 2 61050i3 [1,1,0,-1688450,-845137500] 2 61050i4 [1,1,0,-27014950,-54056114000] 2
61050j (1 curve)	0	2+ 3+ 5- 11+ 37+	2+ 3+ 5-  0 11+  4  5  6
Curve Equation t 61050j1 [1,1,0,-905,-10875] 1
61050k (1 curve)	1	2+ 3+ 5- 11+ 37-	2+ 3+ 5-  2 11+ -5 -3 -4
Curve Equation t Generators 61050k1 [1,1,0,-17075,847125] 1 [85:95:1]
61050l (1 curve)	1	2+ 3+ 5- 11+ 37-	2+ 3+ 5-  3 11+  2 -6 -1
Curve Equation t Generators 61050l1 [1,1,0,-3325,77125] 1 [-39:406:1]
61050m (1 curve)	1	2+ 3+ 5- 11+ 37-	2+ 3+ 5- -5 11+  1  7 -2
Curve Equation t Generators 61050m1 [1,1,0,-3140,-68400] 1 [-35:30:1]
61050n (1 curve)	1	2+ 3+ 5- 11- 37+	2+ 3+ 5- -1 11-  4  6 -3
Curve Equation t Generators 61050n1 [1,1,0,-26825,2045175] 1 [5342:131775:8]
61050o (2 curves)	1	2+ 3+ 5- 11- 37+	2+ 3+ 5-  2 11-  1 -3  0
Curve Equation t Generators 61050o1 [1,1,0,-275875,-55812425] 1 [-19116:24199:64] 61050o2 [1,1,0,-8391950,9350476500] 1 [98644:524679:64]
61050p (1 curve)	1	2+ 3+ 5- 11- 37+	2+ 3+ 5-  3 11- -4 -2 -7
Curve Equation t Generators 61050p1 [1,1,0,-101083075,-516497517875] 1 [12285:303620:1]
61050q (1 curve)	1	2+ 3+ 5- 11- 37+	2+ 3+ 5- -3 11-  4  2 -5
Curve Equation t Generators 61050q1 [1,1,0,-239575,45047125] 1 [285:-5:1]
61050r (1 curve)	0	2+ 3+ 5- 11- 37-	2+ 3+ 5- -1 11-  7 -5 -6
Curve Equation t 61050r1 [1,1,0,-41200,-3236000] 1
61050s (2 curves)	0	2+ 3+ 5- 11- 37-	2+ 3+ 5-  2 11- -2 -2  6
Curve Equation t 61050s1 [1,1,0,-6334950,5938276500] 2 61050s2 [1,1,0,-16014950,-16567723500] 2
61050t (1 curve)	0	2+ 3+ 5- 11- 37-	2+ 3+ 5-  2 11-  4  4  1
Curve Equation t 61050t1 [1,1,0,-325100,-71488800] 1
61050u (1 curve)	0	2+ 3+ 5- 11- 37-	2+ 3+ 5-  4 11-  4  1 -2
Curve Equation t 61050u1 [1,1,0,90175,88747125] 1
61050v (2 curves)	0	2+ 3- 5+ 11+ 37+	2+ 3- 5+ -2 11+  2  6  2
Curve Equation t 61050v1 [1,0,1,-8276,135698] 2 61050v2 [1,0,1,28724,1023698] 2
61050w (1 curve)	0	2+ 3- 5+ 11+ 37+	2+ 3- 5+ -2 11+  5  0  5
Curve Equation t 61050w1 [1,0,1,318174,-814586132] 1
61050x (1 curve)	1	2+ 3- 5+ 11+ 37-	2+ 3- 5+  3 11+ -6  2  7
Curve Equation t Generators 61050x1 [1,0,1,2799,104548] 1 [112018:37435442:1]
61050y (1 curve)	1	2+ 3- 5+ 11+ 37-	2+ 3- 5+ -3 11+  3  5  4
Curve Equation t Generators 61050y1 [1,0,1,-30026,-1755052] 1 [-78:376:1]
61050z (1 curve)	1	2+ 3- 5+ 11- 37+	2+ 3- 5+  2 11-  0  0 -1
Curve Equation t Generators 61050z1 [1,0,1,-129826,53857268] 1 [-179:8537:1]
61050ba (4 curves)	0	2+ 3- 5+ 11- 37-	2+ 3- 5+  0 11- -2 -2 -4
Curve Equation t 61050ba1 [1,0,1,-79526,-8638552] 2 61050ba2 [1,0,1,-80026,-8524552] 4 61050ba3 [1,0,1,13724,-27274552] 2 61050ba4 [1,0,1,-181776,17523448] 2
61050bb (1 curve)	0	2+ 3- 5+ 11- 37-	2+ 3- 5+  0 11-  4 -5  8
Curve Equation t 61050bb1 [1,0,1,949,-5002] 1
61050bc (1 curve)	0	2+ 3- 5+ 11- 37-	2+ 3- 5+  3 11-  1 -5 -4
Curve Equation t 61050bc1 [1,0,1,-853276,303300698] 1
61050bd (1 curve)	0	2+ 3- 5+ 11- 37-	2+ 3- 5+ -3 11-  1  7  8
Curve Equation t 61050bd1 [1,0,1,-312001,-66160102] 1
61050be (1 curve)	1	2+ 3- 5- 11+ 37+	2+ 3- 5- -1 11+  1  3  2
Curve Equation t Generators 61050be1 [1,0,1,-159451,-23427202] 1 [-248:1061:1]
61050bf (1 curve)	0	2+ 3- 5- 11- 37+	2+ 3- 5-  0 11-  7 -2  1
Curve Equation t 61050bf1 [1,0,1,-2201,-61702] 1
61050bg (1 curve)	0	2+ 3- 5- 11- 37+	2+ 3- 5-  3 11- -1  3 -2
Curve Equation t 61050bg1 [1,0,1,-40701,1129048] 1
61050bh (2 curves)	1	2+ 3- 5- 11- 37-	2+ 3- 5- -4 11-  5  3  2
Curve Equation t Generators 61050bh1 [1,0,1,-76951,4030298] 3 [-132:3514:1] 61050bh2 [1,0,1,-3026326,-2026500952] 1 [-63948:46363:64]
61050bi (1 curve)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+  1 11+ -3  3  4
Curve Equation t 61050bi1 [1,1,1,-1898614713,-31843013250969] 1
61050bj (2 curves)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+  2 11+  2 -2  4
Curve Equation t 61050bj1 [1,1,1,-1388,-31219] 2 61050bj2 [1,1,1,-25388,-1567219] 2
61050bk (2 curves)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+  2 11+ -4 -2 -8
Curve Equation t 61050bk1 [1,1,1,-923638,328676531] 2 61050bk2 [1,1,1,445362,1221264531] 2
61050bl (2 curves)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+ -2 11+ -2  3  2
Curve Equation t 61050bl1 [1,1,1,-2317588,1358455781] 1 61050bl2 [1,1,1,3052037,6279030281] 1
61050bm (2 curves)	2	2- 3+ 5+ 11+ 37+	2- 3+ 5+ -2 11+ -6 -6 -2
Curve Equation t Generators 61050bm1 [1,1,1,-6338,142031] 2 [-85:317:1]&[-75:487:1] 61050bm2 [1,1,1,15662,934031] 2 [-45:397:1]&[-31:663:1]
61050bn (4 curves)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+ -4 11+  6  2  4
Curve Equation t 61050bn1 [1,1,1,-1422713,863737031] 2 61050bn2 [1,1,1,-24750713,47379769031] 4 61050bn3 [1,1,1,-26748713,39279877031] 2 61050bn4 [1,1,1,-396000713,3032972269031] 2
61050bo (1 curve)	0	2- 3+ 5+ 11+ 37+	2- 3+ 5+  5 11+ -3 -1  4
Curve Equation t 61050bo1 [1,1,1,-463,-3469] 1
61050bp (1 curve)	1	2- 3+ 5+ 11+ 37-	2- 3+ 5+  2 11+ -6  3  6
Curve Equation t Generators 61050bp1 [1,1,1,-4813,1694531] 1 [175:2412:1]
61050bq (2 curves)	1	2- 3+ 5+ 11- 37+	2- 3+ 5+  4 11- -5 -3  2
Curve Equation t Generators 61050bq1 [1,1,1,-3078,31011] 1 [-51:267:1] 61050bq2 [1,1,1,-121053,-16260429] 1 [-201:132:1]
61050br (1 curve)	0	2- 3+ 5+ 11- 37-	2- 3+ 5+  0 11- -7  2  1
Curve Equation t 61050br1 [1,1,1,-88,-529] 1
61050bs (1 curve)	1	2- 3+ 5- 11+ 37+	2- 3+ 5- -3 11+  6 -2  7
Curve Equation t Generators 61050bs1 [1,1,1,112,881] 1 [5:-43:1]
61050bt (1 curve)	0	2- 3+ 5- 11+ 37-	2- 3+ 5-  1 11+ -1 -3  2
Curve Equation t 61050bt1 [1,1,1,-6378,-189969] 1
61050bu (1 curve)	0	2- 3+ 5- 11+ 37-	2- 3+ 5-  2 11+ -5  0  5
Curve Equation t 61050bu1 [1,1,1,7954362,-101823266469] 1
61050bv (1 curve)	1	2- 3+ 5- 11- 37-	2- 3+ 5- -2 11-  0  0 -1
Curve Equation t Generators 61050bv1 [1,1,1,-3245638,6732158531] 1 [-565:91857:1]
61050bw (1 curve)	1	2- 3+ 5- 11- 37-	2- 3+ 5- -3 11-  1 -3 -2
Curve Equation t Generators 61050bw1 [1,1,1,-1628,8381] 1 [-25:197:1]
61050bx (4 curves)	1	2- 3- 5+ 11+ 37+	2- 3- 5+  0 11+ -2 -6 -4
Curve Equation t Generators 61050bx1 [1,0,0,13562,-7428508] 2 [272:3914:1] 61050bx2 [1,0,0,-498438,-130820508] 4 [-438:2094:1] 61050bx3 [1,0,0,-1290438,387939492] 2 [1278:28110:1] 61050bx4 [1,0,0,-7898438,-8544620508] 2 [-1622:910:1]
61050by (1 curve)	1	2- 3- 5+ 11+ 37+	2- 3- 5+ -2 11+  5  3 -4
Curve Equation t Generators 61050by1 [1,0,0,-683,6777] 1 [28:85:1]
61050bz (1 curve)	1	2- 3- 5+ 11+ 37+	2- 3- 5+ -3 11+ -2  6 -1
Curve Equation t Generators 61050bz1 [1,0,0,-133,617] 1 [8:5:1]
61050ca (4 curves)	0	2- 3- 5+ 11+ 37-	2- 3- 5+  0 11+  6  2  4
Curve Equation t 61050ca1 [1,0,0,-3713,81417] 2 61050ca2 [1,0,0,-11713,-390583] 4 61050ca3 [1,0,0,25287,-2351583] 2 61050ca4 [1,0,0,-176713,-28605583] 2
61050cb (2 curves)	0	2- 3- 5+ 11+ 37-	2- 3- 5+  2 11+  6  2 -2
Curve Equation t 61050cb1 [1,0,0,-21313,1194617] 2 61050cb2 [1,0,0,-15813,1827117] 2
61050cc (2 curves)	0	2- 3- 5+ 11+ 37-	2- 3- 5+  2 11+  6 -6 -6
Curve Equation t 61050cc1 [1,0,0,-458063,-119173383] 2 61050cc2 [1,0,0,-310063,-197465383] 2
61050cd (2 curves)	0	2- 3- 5+ 11+ 37-	2- 3- 5+  2 11+ -6  2 -2
Curve Equation t 61050cd1 [1,0,0,-229088,36897792] 2 61050cd2 [1,0,0,362912,196145792] 2
61050ce (1 curve)	0	2- 3- 5+ 11+ 37-	2- 3- 5+  3 11+  5 -5  4
Curve Equation t 61050ce1 [1,0,0,-82963,-9087583] 1
61050cf (2 curves)	0	2- 3- 5+ 11- 37+	2- 3- 5+ -2 11- -2  6  0
Curve Equation t 61050cf1 [1,0,0,112,1392] 2 61050cf2 [1,0,0,-1388,17892] 2
61050cg (1 curve)	0	2- 3- 5+ 11- 37+	2- 3- 5+ -2 11- -4 -4  1
Curve Equation t 61050cg1 [1,0,0,-8127513,-8919844983] 1
61050ch (2 curves)	0	2- 3- 5+ 11- 37+	2- 3- 5+ -2 11-  6  2  6
Curve Equation t 61050ch1 [1,0,0,-11913,-496683] 2 61050ch2 [1,0,0,-2663,-1245933] 2
61050ci (1 curve)	0	2- 3- 5+ 11- 37+	2- 3- 5+  4 11-  4 -3  0
Curve Equation t 61050ci1 [1,0,0,-37413,-18710433] 1
61050cj (4 curves)	0	2- 3- 5+ 11- 37+	2- 3- 5+  4 11- -6  2  0
Curve Equation t 61050cj1 [1,0,0,-569663,142673817] 2 61050cj2 [1,0,0,-8761663,9981265817] 4 61050cj3 [1,0,0,-8409663,10820081817] 2 61050cj4 [1,0,0,-140185663,638845105817] 2
61050ck (4 curves)	1	2- 3- 5+ 11- 37-	2- 3- 5+  0 11- -2  2 -4
Curve Equation t Generators 61050ck1 [1,0,0,-758507838,8027929652292] 4 [29372:3315314:1] 61050ck2 [1,0,0,-1006315838,2334045236292] 4 [892:1198354:1] 61050ck3 [1,0,0,3943684162,18495795236292] 2 [816624:3489279470:729] 61050ck4 [1,0,0,-9921243838,-378235316155708] 2 [504858888:-415779773194:729]
61050cl (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+  1 11- -1  3  0
Curve Equation t Generators 61050cl1 [1,0,0,-1415438,272703492] 1 [-68:-19166:1]
61050cm (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+  1 11- -4 -6 -3
Curve Equation t Generators 61050cm1 [1,0,0,-670638,256988142] 1 [5214:76125:8]
61050cn (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+ -1 11-  3 -3  0
Curve Equation t Generators 61050cn1 [1,0,0,-20438,1119492] 1 [22:814:1]
61050co (2 curves)	1	2- 3- 5+ 11- 37-	2- 3- 5+ -2 11- -1  3  0
Curve Equation t Generators 61050co1 [1,0,0,-335678,74803812] 5 [-542:10150:1] 61050co2 [1,0,0,-6896888,-6962759358] 1 [-12121980:30505641:8000]
61050cp (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+ -2 11-  2  3 -6
Curve Equation t Generators 61050cp1 [1,0,0,187,1617] 1 [12:69:1]
61050cq (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+  3 11- -4 -2 -5
Curve Equation t Generators 61050cq1 [1,0,0,-9583,360377] 1 [46:109:1]
61050cr (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+ -3 11-  4  2 -7
Curve Equation t Generators 61050cr1 [1,0,0,-4043323,-4131980143] 1 [4958:-315055:1]
61050cs (1 curve)	1	2- 3- 5+ 11- 37-	2- 3- 5+ -3 11- -5  5 -4
Curve Equation t Generators 61050cs1 [1,0,0,-23611588,39078347792] 1 [-3718:276584:1]
61050ct (1 curve)	2	2- 3- 5- 11+ 37+	2- 3- 5- -4 11+ -5 -7 -6
Curve Equation t Generators 61050ct1 [1,0,0,-33988,2354192] 1 [-208:764:1]&[452:-9136:1]
61050cu (1 curve)	0	2- 3- 5- 11+ 37+	2- 3- 5-  5 11+ -1 -7 -2
Curve Equation t 61050cu1 [1,0,0,-78513,-8392983] 1
61050cv (1 curve)	1	2- 3- 5- 11+ 37-	2- 3- 5-  0 11+ -4 -5  6
Curve Equation t Generators 61050cv1 [1,0,0,-22638,-1314108] 1 [252:2874:1]
61050cw (1 curve)	1	2- 3- 5- 11+ 37-	2- 3- 5- -2 11+  0  0 -1
Curve Equation t Generators 61050cw1 [1,0,0,912,-4608] 1 [72:-696:1]
61050cx (2 curves)	1	2- 3- 5- 11+ 37-	2- 3- 5- -4 11+  5 -6 -1
Curve Equation t Generators 61050cx1 [1,0,0,49312,-19012608] 3 [676:17644:1] 61050cx2 [1,0,0,-4162688,-3271259808] 1 [4876:-306356:1]
61050cy (1 curve)	1	2- 3- 5- 11- 37+	2- 3- 5-  1 11- -7  5 -6
Curve Equation t Generators 61050cy1 [1,0,0,-1648,-25888] 1 [-636:328:27]
61050cz (2 curves)	1	2- 3- 5- 11- 37+	2- 3- 5- -2 11-  2  2  6
Curve Equation t Generators 61050cz1 [1,0,0,-253398,47506212] 2 [-372:9690:1] 61050cz2 [1,0,0,-640598,-132541788] 2 [-482:8260:1]
61050da (1 curve)	1	2- 3- 5- 11- 37+	2- 3- 5- -4 11- -4 -1 -2
Curve Equation t Generators 61050da1 [1,0,0,3607,709977] 1 [322:-6101:1]
61050db (1 curve)	0	2- 3- 5- 11- 37-	2- 3- 5-  0 11- -7 -3  6
Curve Equation t 61050db1 [1,0,0,-88,242] 1

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

Part of Computational Number Theory
Back to Tables and computations