Cremona's table of elliptic curves

588 = 2² · 3 · 7²

Class	r	Atkin-Lehner	Eigenvalues
588a (1 curve)	0	2- 3+ 7+	2- 3+ -2 7+  2 -3  8 -1
Curve Equation t 588a1 [0,-1,0,131,-167] 1
588b (4 curves)	1	2- 3+ 7-	2- 3+  0 7- -6 -2  0  4
Curve Equation t Generators 588b1 [0,-1,0,327,666] 2 [5:49:1] 588b2 [0,-1,0,-1388,6840] 2 [-2:98:1] 588b3 [0,-1,0,-5553,165894] 2 [26:196:1] 588b4 [0,-1,0,-89588,10350936] 2 [257:2058:1]
588c (2 curves)	1	2- 3+ 7-	2- 3+ -2 7-  2  4 -6 -8
Curve Equation t Generators 588c1 [0,-1,0,-9,-6] 2 [-1:1:1] 588c2 [0,-1,0,-44,120] 2 [-2:14:1]
588d (1 curve)	0	2- 3- 7-	2- 3-  2 7-  2  3 -8  1
Curve Equation t 588d1 [0,1,0,6403,44463] 1
588e (2 curves)	0	2- 3- 7-	2- 3-  2 7-  2 -4  6  8
Curve Equation t 588e1 [0,1,0,-457,2960] 2 588e2 [0,1,0,-2172,-36828] 2
588f (2 curves)	0	2- 3- 7-	2- 3- -4 7-  2  6  4  4
Curve Equation t 588f1 [0,1,0,-65,804] 2 588f2 [0,1,0,-1780,28244] 2

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

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