Cremona's table of elliptic curves

69030 = 2 · 3² · 5 · 13 · 59

Class	r	Atkin-Lehner	Eigenvalues
69030a (2 curves)	0	2+ 3+ 5+ 13+ 59-	2+ 3+ 5+  2 -4 13+  0 -2
Curve Equation t 69030a1 [1,-1,0,-5734545,-5363488675] 2 69030a2 [1,-1,0,-92134545,-340370848675] 2
69030b (1 curve)	0	2+ 3+ 5+ 13- 59+	2+ 3+ 5+ -1 -3 13-  2 -5
Curve Equation t 69030b1 [1,-1,0,-4875,-124219] 1
69030c (1 curve)	0	2+ 3+ 5- 13+ 59+	2+ 3+ 5- -1  1 13+ -2  3
Curve Equation t 69030c1 [1,-1,0,-87042939,312592572773] 1
69030d (2 curves)	1	2+ 3+ 5- 13- 59+	2+ 3+ 5- -2  4 13-  6 -8
Curve Equation t Generators 69030d1 [1,-1,0,-678444,-216242992] 2 [4219:266230:1] 69030d2 [1,-1,0,-10873644,-13798288432] 2 [6446209:285704450:1331]
69030e (2 curves)	1	2+ 3+ 5- 13- 59+	2+ 3+ 5-  5 -3 13- -6 -7
Curve Equation t Generators 69030e1 [1,-1,0,-229749,42305805] 3 [51:5517:1] 69030e2 [1,-1,0,-1214124,-481622320] 1 [-719:4747:1]
69030f (2 curves)	0	2+ 3+ 5- 13- 59-	2+ 3+ 5-  4  0 13-  2  0
Curve Equation t 69030f1 [1,-1,0,-556959,-159847987] 2 69030f2 [1,-1,0,-8911359,-10236925267] 2
69030g (2 curves)	0	2+ 3+ 5- 13- 59-	2+ 3+ 5-  4  4 13-  4 -2
Curve Equation t 69030g1 [1,-1,0,-104964,-13584880] 2 69030g2 [1,-1,0,-1697964,-851184280] 2
69030h (1 curve)	0	2+ 3- 5+ 13+ 59+	2+ 3- 5+  3  1 13+  6 -5
Curve Equation t 69030h1 [1,-1,0,-2520,43200] 1
69030i (1 curve)	1	2+ 3- 5+ 13+ 59-	2+ 3- 5+  0  2 13+ -6 -5
Curve Equation t Generators 69030i1 [1,-1,0,270,-2484] 1 [309:1055:27]
69030j (1 curve)	1	2+ 3- 5+ 13+ 59-	2+ 3- 5+ -3 -3 13+ -4 -6
Curve Equation t Generators 69030j1 [1,-1,0,-10260,-609584] 1 [200:2204:1]
69030k (1 curve)	1	2+ 3- 5+ 13- 59+	2+ 3- 5+  1 -1 13-  8 -2
Curve Equation t Generators 69030k1 [1,-1,0,-2355,214325] 1 [-2:469:1]
69030l (1 curve)	1	2+ 3- 5+ 13- 59+	2+ 3- 5+ -1  3 13-  2  1
Curve Equation t Generators 69030l1 [1,-1,0,-56025,1062661] 1 [-85:2324:1]
69030m (4 curves)	0	2+ 3- 5+ 13- 59-	2+ 3- 5+  0  4 13- -6  0
Curve Equation t 69030m1 [1,-1,0,-2925,50085] 2 69030m2 [1,-1,0,-14445,-620379] 4 69030m3 [1,-1,0,13635,-2760075] 2 69030m4 [1,-1,0,-226845,-41528619] 2
69030n (4 curves)	0	2+ 3- 5+ 13- 59-	2+ 3- 5+  2  0 13- -6 -4
Curve Equation t 69030n1 [1,-1,0,-18585,-1221075] 2 69030n2 [1,-1,0,-318105,-68972499] 2 69030n3 [1,-1,0,139815,11384685] 6 69030n4 [1,-1,0,-651105,98227701] 6
69030o (1 curve)	1	2+ 3- 5- 13+ 59+	2+ 3- 5-  0 -2 13+  6  1
Curve Equation t Generators 69030o1 [1,-1,0,-5487849,4950265293] 1 [8966:110497:8]
69030p (4 curves)	1	2+ 3- 5- 13+ 59+	2+ 3- 5-  0  4 13+ -6  4
Curve Equation t Generators 69030p1 [1,-1,0,-485379,-130036347] 2 [1902:75369:1] 69030p2 [1,-1,0,-485559,-129934935] 4 [-3282:4071:8] 69030p3 [1,-1,0,-342189,-208300977] 2 [8046:168327:8] 69030p4 [1,-1,0,-631809,-45080685] 2 [59118:5022411:8]
69030q (1 curve)	1	2+ 3- 5- 13+ 59+	2+ 3- 5-  1  5 13+  6 -3
Curve Equation t Generators 69030q1 [1,-1,0,-32724,1998918] 1 [57:534:1]
69030r (1 curve)	1	2+ 3- 5- 13+ 59+	2+ 3- 5- -1  3 13+  2  4
Curve Equation t Generators 69030r1 [1,-1,0,36,-320] 1 [20:80:1]
69030s (1 curve)	1	2+ 3- 5- 13+ 59+	2+ 3- 5- -4  0 13+ -4  7
Curve Equation t Generators 69030s1 [1,-1,0,-1347264,-601567232] 1 [1984717394667577890343968467738484735:205049280696579339365555309373731372266:181972317266530678915014530394125]
69030t (1 curve)	1	2+ 3- 5- 13+ 59+	2+ 3- 5- -5  3 13+  6  1
Curve Equation t Generators 69030t1 [1,-1,0,-4045192524,-98758438621232] 1 [-35863:451484:1]
69030u (2 curves)	0	2+ 3- 5- 13+ 59-	2+ 3- 5-  0  4 13+  0  2
Curve Equation t 69030u1 [1,-1,0,1791,256365] 2 69030u2 [1,-1,0,-51309,4302585] 2
69030v (1 curve)	0	2+ 3- 5- 13+ 59-	2+ 3- 5-  1  3 13+  2 -5
Curve Equation t 69030v1 [1,-1,0,-10563354,-13178833772] 1
69030w (2 curves)	2	2+ 3- 5- 13+ 59-	2+ 3- 5- -2  0 13+ -6  0
Curve Equation t Generators 69030w1 [1,-1,0,-41499,44928805] 2 [-319:5222:1]&[86:-6523:1] 69030w2 [1,-1,0,-2165499,1217801605] 2 [-859:49862:1]&[7278:-1549:8]
69030x (2 curves)	1	2+ 3- 5- 13- 59-	2+ 3- 5- -1 -3 13-  0  2
Curve Equation t Generators 69030x1 [1,-1,0,9126,325620] 1 [84:1254:1] 69030x2 [1,-1,0,-238734,45299088] 3 [282:-726:1]
69030y (1 curve)	1	2- 3+ 5+ 13+ 59-	2- 3+ 5+ -1 -1 13+  2  3
Curve Equation t Generators 69030y1 [1,-1,1,-9671438,-11574278883] 1 [-1795:903:1]
69030z (2 curves)	1	2- 3+ 5+ 13- 59+	2- 3+ 5+  4  0 13- -2  0
Curve Equation t Generators 69030z1 [1,-1,1,-5012633,4320908281] 2 [1303:-4:1] 69030z2 [1,-1,1,-80202233,276477184441] 2 [4381:93632:1]
69030ba (2 curves)	1	2- 3+ 5+ 13- 59+	2- 3+ 5+  4 -4 13- -4 -2
Curve Equation t Generators 69030ba1 [1,-1,1,-11663,507031] 2 [-7:770:1] 69030ba2 [1,-1,1,-188663,31588231] 2 [241:152:1]
69030bb (2 curves)	2	2- 3+ 5+ 13- 59-	2- 3+ 5+ -2 -4 13- -6 -8
Curve Equation t Generators 69030bb1 [1,-1,1,-75383,8034127] 2 [5601:-33494:27]&[-197:3998:1] 69030bb2 [1,-1,1,-1208183,511450447] 2 [-1013:26870:1]&[625:116:1]
69030bc (2 curves)	0	2- 3+ 5+ 13- 59-	2- 3+ 5+  5  3 13-  6 -7
Curve Equation t 69030bc1 [1,-1,1,-134903,17882831] 3 69030bc2 [1,-1,1,-2067743,-1140188993] 1
69030bd (2 curves)	1	2- 3+ 5- 13+ 59+	2- 3+ 5-  2  4 13+  0 -2
Curve Equation t Generators 69030bd1 [1,-1,1,-637172,198860119] 2 [-283:19021:1] 69030bd2 [1,-1,1,-10237172,12609740119] 2 [1837:-139:1]
69030be (1 curve)	1	2- 3+ 5- 13- 59-	2- 3+ 5- -1  3 13- -2 -5
Curve Equation t Generators 69030be1 [1,-1,1,-542,4781] 1 [9:19:1]
69030bf (4 curves)	1	2- 3- 5+ 13+ 59+	2- 3- 5+  0 -4 13+ -2  0
Curve Equation t Generators 69030bf1 [1,-1,1,1867,98381] 2 [15:-368:1] 69030bf2 [1,-1,1,-24053,1311437] 4 [-125:1596:1] 69030bf3 [1,-1,1,-87773,-8552419] 2 [-179:1272:1] 69030bf4 [1,-1,1,-375053,88499837] 2 [357:-80:1]
69030bg (1 curve)	1	2- 3- 5+ 13+ 59+	2- 3- 5+  3  3 13+ -2  7
Curve Equation t Generators 69030bg1 [1,-1,1,-68,101] 1 [-66:83:8]
69030bh (1 curve)	0	2- 3- 5+ 13+ 59-	2- 3- 5+  1 -1 13+  2  1
Curve Equation t 69030bh1 [1,-1,1,-15233,-719503] 1
69030bi (2 curves)	0	2- 3- 5+ 13+ 59-	2- 3- 5+  2  0 13+ -6  4
Curve Equation t 69030bi1 [1,-1,1,-23,587] 2 69030bi2 [1,-1,1,-1193,16031] 2
69030bj (2 curves)	0	2- 3- 5+ 13+ 59-	2- 3- 5+  2 -4 13+ -4  6
Curve Equation t 69030bj1 [1,-1,1,-2599628,-1635975669] 2 69030bj2 [1,-1,1,-41760878,-103862502669] 2
69030bk (1 curve)	0	2- 3- 5+ 13+ 59-	2- 3- 5+ -3  5 13+ -6  4
Curve Equation t 69030bk1 [1,-1,1,-13497593,-25922530663] 1
69030bl (2 curves)	2	2- 3- 5+ 13+ 59-	2- 3- 5+ -4 -4 13+  4  2
Curve Equation t Generators 69030bl1 [1,-1,1,-2948,106647] 2 [-57:323:1]&[-37:423:1] 69030bl2 [1,-1,1,-56048,5119287] 2 [766:5931:8]&[125:171:1]
69030bm (2 curves)	1	2- 3- 5+ 13- 59-	2- 3- 5+ -2  0 13- -6  0
Curve Equation t Generators 69030bm1 [1,-1,1,-35393,2573457] 2 [83:408:1] 69030bm2 [1,-1,1,-566393,164209857] 2 [437:-300:1]
69030bn (1 curve)	1	2- 3- 5+ 13- 59-	2- 3- 5+  4  0 13-  0 -7
Curve Equation t Generators 69030bn1 [1,-1,1,-293,-7459] 1 [31:96:1]
69030bo (2 curves)	1	2- 3- 5- 13- 59+	2- 3- 5- -1  3 13- -6 -1
Curve Equation t Generators 69030bo1 [1,-1,1,-9302,-313531] 1 [-51:187:1] 69030bo2 [1,-1,1,-160637,24766661] 3 [-249:7144:1]
69030bp (4 curves)	0	2- 3- 5- 13- 59-	2- 3- 5-  0 -4 13- -2  0
Curve Equation t 69030bp1 [1,-1,1,-37202,-3940671] 4 69030bp2 [1,-1,1,-663782,-207955119] 4 69030bp3 [1,-1,1,-732812,-162008751] 2 69030bp4 [1,-1,1,-10620032,-13318345119] 2
69030bq (2 curves)	0	2- 3- 5- 13- 59-	2- 3- 5- -1 -3 13-  6  8
Curve Equation t 69030bq1 [1,-1,1,-1083767,-433991041] 1 69030bq2 [1,-1,1,-1055102,-458054899] 3
69030br (1 curve)	0	2- 3- 5- 13- 59-	2- 3- 5-  3  5 13- -2 -3
Curve Equation t 69030br1 [1,-1,1,-159647,-24485241] 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