Cremona's table of elliptic curves

550 = 2 · 5² · 11

Class	r	Atkin-Lehner	Eigenvalues
550a (2 curves)	1	2+ 5+ 11+	2+ -1 5+  1 11+ -2  3 -1
Curve Equation t Generators 550a1 [1,1,0,-25,125] 1 [5:10:1] 550a2 [1,1,0,225,-3125] 1 [15:55:1]
550b (2 curves)	0	2+ 5+ 11-	2+  1 5+ -3 11-  6  7  5
Curve Equation t 550b1 [1,0,1,249,-6102] 1 550b2 [1,0,1,-148501,-22038602] 1
550c (1 curve)	0	2+ 5+ 11-	2+ -2 5+  0 11- -3  4 -1
Curve Equation t 550c1 [1,0,1,-206,-1152] 1
550d (2 curves)	0	2+ 5- 11+	2+ -2 5- -4 11+  5  0 -7
Curve Equation t 550d1 [1,0,1,49,48] 3 550d2 [1,0,1,-576,-6202] 1
550e (1 curve)	0	2+ 5- 11+	2+  3 5-  1 11+  0  5 -7
Curve Equation t 550e1 [1,-1,0,-367,10541] 1
550f (3 curves)	1	2+ 5- 11-	2+  1 5- -3 11- -4 -3 -5
Curve Equation t Generators 550f1 [1,0,1,-701,-7202] 1 [52:286:1] 550f2 [1,0,1,4924,75298] 1 [52:661:1] 550f3 [1,0,1,-758201,254051548] 1 [502:-189:1]
550g (2 curves)	1	2+ 5- 11-	2+ -2 5-  0 11-  2 -6  4
Curve Equation t Generators 550g1 [1,0,1,-6,8] 2 [1:1:1] 550g2 [1,0,1,-106,408] 2 [3:9:1]
550h (2 curves)	0	2- 5+ 11+	2-  2 5+  4 11+ -5  0 -7
Curve Equation t 550h1 [1,1,1,2,1] 1 550h2 [1,1,1,-23,-59] 1
550i (2 curves)	1	2- 5+ 11-	2- -1 5+ -5 11- -2 -3 -7
Curve Equation t Generators 550i1 [1,1,1,-2213,39531] 1 [-35:292:1] 550i2 [1,1,1,7412,212781] 1 [5:497:1]
550j (1 curve)	1	2- 5- 11+	2- -3 5- -1 11+  0 -5 -7
Curve Equation t Generators 550j1 [1,-1,1,-15,87] 1 [-1:10:1]
550k (3 curves)	0	2- 5- 11-	2- -1 5-  3 11-  4  3 -5
Curve Equation t 550k1 [1,1,1,-28,-69] 1 550k2 [1,1,1,197,681] 5 550k3 [1,1,1,-30328,2020281] 5
550l (2 curves)	0	2- 5- 11-	2-  2 5-  0 11- -2  6  4
Curve Equation t 550l1 [1,1,1,-138,1031] 2 550l2 [1,1,1,-2638,51031] 2
550m (1 curve)	0	2- 5- 11-	2-  2 5-  0 11-  3 -4 -1
Curve Equation t 550m1 [1,1,1,-5138,-143969] 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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