Cremona's table of elliptic curves

672 = 2⁵ · 3 · 7

Class	r	Atkin-Lehner	Eigenvalues
672a (2 curves)	1	2+ 3+ 7+	2+ 3+  0 7+ -2 -2  4 -4
Curve Equation t Generators 672a1 [0,-1,0,2,4] 2 [0:2:1] 672a2 [0,-1,0,-33,81] 2 [-3:12:1]
672b (2 curves)	1	2+ 3- 7-	2+ 3- -4 7- -2 -2  0 -4
Curve Equation t Generators 672b1 [0,1,0,210,1764] 2 [0:42:1] 672b2 [0,1,0,-1505,17199] 2 [175:-2268:1]
672c (4 curves)	0	2- 3+ 7+	2- 3+  2 7+  0  2  2  4
Curve Equation t 672c1 [0,-1,0,-22,40] 4 672c2 [0,-1,0,-112,-392] 2 672c3 [0,-1,0,-337,2497] 4 672c4 [0,-1,0,48,180] 2
672d (2 curves)	0	2- 3+ 7+	2- 3+ -4 7+  2 -2  0  4
Curve Equation t 672d1 [0,-1,0,210,-1764] 2 672d2 [0,-1,0,-1505,-17199] 2
672e (4 curves)	1	2- 3+ 7-	2- 3+ -2 7-  4 -6 -2 -4
Curve Equation t Generators 672e1 [0,-1,0,-14,24] 4 [-1:6:1] 672e2 [0,-1,0,-49,-95] 2 [-3:4:1] 672e3 [0,-1,0,-224,1368] 2 [13:22:1] 672e4 [0,-1,0,16,84] 4 [1:10:1]
672f (4 curves)	1	2- 3- 7+	2- 3- -2 7+ -4 -6 -2  4
Curve Equation t Generators 672f1 [0,1,0,-14,-24] 4 [6:12:1] 672f2 [0,1,0,-224,-1368] 2 [27:114:1] 672f3 [0,1,0,-49,95] 4 [-7:12:1] 672f4 [0,1,0,16,-84] 2 [42:105:8]
672g (2 curves)	0	2- 3- 7-	2- 3-  0 7-  2 -2  4  4
Curve Equation t 672g1 [0,1,0,2,-4] 2 672g2 [0,1,0,-33,-81] 2
672h (4 curves)	0	2- 3- 7-	2- 3-  2 7-  0  2  2 -4
Curve Equation t 672h1 [0,1,0,-22,-40] 4 672h2 [0,1,0,-337,-2497] 2 672h3 [0,1,0,-112,392] 4 672h4 [0,1,0,48,-180] 2

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

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