Cremona's table of elliptic curves

51615 = 3² · 5 · 31 · 37

Class	r	Atkin-Lehner	Eigenvalues
51615a (2 curves)	0	3+ 5+ 31- 37+	1 3+ 5+  2 -4  2  2 -4
Curve Equation t 51615a1 [1,-1,0,-420,-1045] 2 51615a2 [1,-1,0,-5415,-151894] 2
51615b (2 curves)	1	3+ 5- 31- 37+	-1 3+ 5-  2  4  2 -2 -4
Curve Equation t Generators 51615b1 [1,-1,1,-47,54] 2 [-6:12:1] 51615b2 [1,-1,1,-602,5826] 2 [-24:89:1]
51615c (4 curves)	1	3- 5+ 31- 37+	1 3- 5+  0  4  2  2  4
Curve Equation t Generators 51615c1 [1,-1,0,-720,7371] 2 [-30:51:1] 51615c2 [1,-1,0,-1845,-20304] 4 [27246:1576119:8] 51615c3 [1,-1,0,5130,-141669] 2 [2282940:-11408139:85184] 51615c4 [1,-1,0,-26820,-1683639] 2 [-2087540:851633:21952]
51615d (1 curve)	2	3- 5+ 31- 37-	-1 3- 5+  1 -2 -3 -2  4
Curve Equation t Generators 51615d1 [1,-1,1,-1148,17322] 1 [-37:108:1]&[-10:171:1]
51615e (1 curve)	1	3- 5- 31+ 37+	0 3- 5-  3 -5 -6  4  2
Curve Equation t Generators 51615e1 [0,0,1,-69942,4312930] 1 [8:1937:1]
51615f (1 curve)	1	3- 5- 31+ 37+	2 3- 5-  2 -2  7  6 -8
Curve Equation t Generators 51615f1 [0,0,1,-507,4495] 1 [82:151:8]
51615g (1 curve)	0	3- 5- 31- 37+	2 3- 5-  2 -2 -1 -2  8
Curve Equation t 51615g1 [0,0,1,28383,550705] 1

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

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