Cremona's table of elliptic curves

585 = 3² · 5 · 13

Class	r	Atkin-Lehner	Eigenvalues
585a (2 curves)	1	3+ 5+ 13+	-1 3+ 5+  2 -4 13+ -4  6
Curve Equation t Generators 585a1 [1,-1,1,-218,1432] 2 [8:8:1] 585a2 [1,-1,1,-3593,83782] 2 [28:53:1]
585b (2 curves)	0	3+ 5+ 13-	0 3+ 5+ -1  3 13-  3 -4
Curve Equation t 585b1 [0,0,1,12,-21] 3 585b2 [0,0,1,-378,-2842] 1
585c (2 curves)	0	3+ 5- 13+	1 3+ 5-  2  4 13+  4  6
Curve Equation t 585c1 [1,-1,0,-24,-45] 2 585c2 [1,-1,0,-399,-2970] 2
585d (2 curves)	1	3+ 5- 13-	0 3+ 5- -1 -3 13- -3 -4
Curve Equation t Generators 585d1 [0,0,1,-42,105] 3 [-7:7:1] 585d2 [0,0,1,108,560] 1 [30:175:1]
585e (1 curve)	0	3- 5+ 13+	-2 3- 5+  3  1 13+  1 -2
Curve Equation t 585e1 [0,0,1,-1713,-28022] 1
585f (8 curves)	1	3- 5+ 13-	1 3- 5+  0 -4 13- -2 -4
Curve Equation t Generators 585f1 [1,-1,0,-990,-11745] 2 [238:3513:1] 585f2 [1,-1,0,-1035,-10584] 4 [40:84:1] 585f3 [1,-1,0,-4680,114075] 4 [78:429:1] 585f4 [1,-1,0,1890,-61479] 2 [230:897:8] 585f5 [1,-1,0,-73125,7629336] 4 [120:696:1] 585f6 [1,-1,0,5445,533250] 2 [-30:600:1] 585f7 [1,-1,0,-1170000,487402461] 2 [588:1281:1] 585f8 [1,-1,0,-71370,8011575] 2 [1038:7167:8]
585g (1 curve)	1	3- 5+ 13-	-2 3- 5+ -3  5 13- -5  2
Curve Equation t Generators 585g1 [0,0,1,-3,18] 1 [-1:4:1]
585h (2 curves)	1	3- 5- 13+	1 3- 5- -4 -2 13+ -2 -6
Curve Equation t Generators 585h1 [1,-1,0,-9,0] 2 [4:2:1] 585h2 [1,-1,0,36,-27] 2 [4:11:1]
585i (1 curve)	1	3- 5- 13+	-2 3- 5- -1 -5 13+  7 -6
Curve Equation t Generators 585i1 [0,0,1,-597,8820] 1 [8:67:1]

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