Cremona's table of elliptic curves

68211 = 3² · 11 · 13 · 53

Class	r	Atkin-Lehner	Eigenvalues
68211a (1 curve)	1	3- 11+ 13+ 53-	0 3-  3 -4 11+ 13+  2  2
Curve Equation t Generators 68211a1 [0,0,1,6984,-280267] 1 [73:786:1]
68211b (4 curves)	1	3- 11+ 13- 53+	1 3-  2  0 11+ 13-  2  4
Curve Equation t Generators 68211b1 [1,-1,0,-4266,108319] 2 [3601640:11638241:64000] 68211b2 [1,-1,0,-4311,105952] 4 [-1516:28973:64] 68211b3 [1,-1,0,2124,390379] 2 [-996:1078463:1728] 68211b4 [1,-1,0,-11466,-330503] 2 [176:1667:1]
68211c (1 curve)	0	3- 11+ 13- 53-	0 3-  1  0 11+ 13-  2  0
Curve Equation t 68211c1 [0,0,1,-33192,-2327866] 1
68211d (1 curve)	0	3- 11- 13- 53+	0 3-  2 -3 11- 13-  0 -4
Curve Equation t 68211d1 [0,0,1,186,-27464] 1
68211e (2 curves)	0	3- 11- 13- 53+	0 3- -3  2 11- 13-  0 -4
Curve Equation t 68211e1 [0,0,1,-3554274,-2581414380] 1 68211e2 [0,0,1,4282836,-11634161265] 3
68211f (2 curves)	2	3- 11- 13- 53+	1 3-  0  0 11- 13- -6  0
Curve Equation t Generators 68211f1 [1,-1,0,-132,1043] 2 [-2:37:1]&[2:27:1] 68211f2 [1,-1,0,-2517,49220] 2 [4:196:1]&[302:515:8]
68211g (2 curves)	2	3- 11- 13- 53+	-1 3- -4  0 11- 13- -2 -8
Curve Equation t Generators 68211g1 [1,-1,1,1813,-76350] 2 [286:1311:8]&[56:-474:1] 68211g2 [1,-1,1,-19652,-934950] 2 [-93:332:1]&[-82:387:1]
68211h (1 curve)	1	3- 11- 13- 53-	-2 3-  2 -1 11- 13-  4 -2
Curve Equation t Generators 68211h1 [0,0,1,-1408449,949223016] 1 [3548:201532:1]

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

Part of Computational Number Theory
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