Cremona's table of elliptic curves

558 = 2 · 3² · 31

Class	r	Atkin-Lehner	Eigenvalues
558a (1 curve)	1	2+ 3+ 31+	2+ 3+ -1  0 -3 -1 -3  1
Curve Equation t Generators 558a1 [1,-1,0,0,2] 1 [1:1:1]
558b (2 curves)	0	2+ 3+ 31-	2+ 3+  3 -4  3  5  3 -7
Curve Equation t 558b1 [1,-1,0,-48,288] 3 558b2 [1,-1,0,417,-6067] 1
558c (4 curves)	0	2+ 3- 31+	2+ 3-  2  0  0  2  6  4
Curve Equation t 558c1 [1,-1,0,-6,-28] 2 558c2 [1,-1,0,-186,-928] 4 558c3 [1,-1,0,-2976,-61750] 2 558c4 [1,-1,0,-276,134] 2
558d (2 curves)	1	2+ 3- 31-	2+ 3- -1 -2  3 -1 -3 -5
Curve Equation t Generators 558d1 [1,-1,0,135,-243] 1 [9:36:1] 558d2 [1,-1,0,-12555,544887] 1 [279:4185:1]
558e (1 curve)	0	2- 3+ 31+	2- 3+  1  0  3 -1  3  1
Curve Equation t 558e1 [1,-1,1,-2,-53] 1
558f (2 curves)	1	2- 3+ 31-	2- 3+ -3 -4 -3  5 -3 -7
Curve Equation t Generators 558f1 [1,-1,1,46,209] 3 [-3:7:1] 558f2 [1,-1,1,-434,-7343] 1 [91:-883:1]
558g (1 curve)	1	2- 3- 31+	2- 3- -3 -2 -5 -7  1  7
Curve Equation t Generators 558g1 [1,-1,1,-149,749] 1 [9:-14:1]
558h (1 curve)	0	2- 3- 31-	2- 3-  1  2 -3  3 -1  7
Curve Equation t 558h1 [1,-1,1,-752,9213] 1

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

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