Cremona's table of elliptic curves

574 = 2 · 7 · 41

Class	r	Atkin-Lehner	Eigenvalues
574a (1 curve)	1	2+ 7+ 41+	2+ -1  1 7+  0  2 -5 -4
Curve Equation t Generators 574a1 [1,1,0,-2,-2] 1 [-1:1:1]
574b (2 curves)	1	2+ 7+ 41+	2+  2 -2 7+ -6 -4 -2  2
Curve Equation t Generators 574b1 [1,1,0,-2061,35165] 2 [17:65:1] 574b2 [1,1,0,-2221,29181] 2 [39:42:1]
574c (2 curves)	0	2+ 7- 41+	2+  2  2 7- -2  4  6 -6
Curve Equation t 574c1 [1,1,0,-84,80] 2 574c2 [1,1,0,-724,-7728] 2
574d (2 curves)	0	2+ 7- 41+	2+ -2  4 7-  4  4 -2 -6
Curve Equation t 574d1 [1,0,1,-31679,5254674] 2 574d2 [1,0,1,-687039,218902034] 2
574e (1 curve)	0	2+ 7- 41+	2+  3 -1 7-  4 -6  3  4
Curve Equation t 574e1 [1,-1,0,-40,-88] 1
574f (2 curves)	1	2+ 7- 41-	2+  1 -3 7-  0  2 -3 -4
Curve Equation t Generators 574f1 [1,0,1,-80,190] 3 [-2:19:1] 574f2 [1,0,1,-2335,-43598] 1 [-28:17:1]
574g (1 curve)	1	2- 7+ 41-	2- -1 -1 7+ -6 -4  7  0
Curve Equation t Generators 574g1 [1,1,1,-21,-5] 1 [-1:4:1]
574h (2 curves)	1	2- 7- 41+	2-  0 -4 7- -2 -6 -6  4
Curve Equation t Generators 574h1 [1,-1,1,3,5] 2 [1:2:1] 574h2 [1,-1,1,-37,85] 2 [1:6:1]
574i (2 curves)	1	2- 7- 41+	2- -3 -1 7- -2  0 -3 -8
Curve Equation t Generators 574i1 [1,-1,1,-19353,958713] 7 [-121:1292:1] 574i2 [1,-1,1,-9611313,-11466507927] 1 [-6040065:3021062:3375]
574j (2 curves)	0	2- 7- 41-	2- -1  1 7-  2  4  3  0
Curve Equation t 574j1 [1,1,1,-175,789] 5 574j2 [1,1,1,-15785,-769911] 1

Data from Elliptic Curve Data by J. E. Cremona.
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