Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Class	r	Atkin-Lehner	Eigenvalues
840a (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  4 -2 -6  0
Curve Equation t Generators 840a1 [0,-1,0,-316,-2060] 2 [54:368:1] 840a2 [0,-1,0,-336,-1764] 4 [-7:14:1] 840a3 [0,-1,0,-1736,26796] 2 [33:66:1] 840a4 [0,-1,0,744,-11700] 2 [209:3038:1]
840b (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0 -2  6 -4
Curve Equation t 840b1 [0,-1,0,9,-84] 4 840b2 [0,-1,0,-236,-1260] 4 840b3 [0,-1,0,-3736,-86660] 2 840b4 [0,-1,0,-656,4956] 2
840c (4 curves)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+  0  2  2  0
Curve Equation t 840c1 [0,-1,0,-15,12] 4 840c2 [0,-1,0,-140,-588] 4 840c3 [0,-1,0,-2240,-40068] 2 840c4 [0,-1,0,-40,-1508] 2
840d (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0  6 -2  4
Curve Equation t 840d1 [0,1,0,-27991,-1811530] 2 840d2 [0,1,0,-31116,-1385280] 4 840d3 [0,1,0,-202616,34012320] 4 840d4 [0,1,0,90384,-9452880] 2
840e (4 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -4  2 -2  0
Curve Equation t Generators 840e1 [0,-1,0,9,0] 2 [1:3:1] 840e2 [0,-1,0,-36,36] 4 [-4:10:1] 840e3 [0,-1,0,-336,-2244] 2 [-10:4:1] 840e4 [0,-1,0,-456,3900] 2 [14:8:1]
840f (6 curves)	1	2- 3+ 5- 7+	2- 3+ 5- 7+ -4 -2  2 -4
Curve Equation t Generators 840f1 [0,-1,0,-175,952] 4 [17:51:1] 840f2 [0,-1,0,-180,900] 8 [-10:40:1] 840f3 [0,-1,0,-680,-5700] 4 [-15:30:1] 840f4 [0,-1,0,240,4092] 4 [-2:60:1] 840f5 [0,-1,0,-10480,-409460] 2 [986:3159:8] 840f6 [0,-1,0,1120,-32340] 2 [57:462:1]
840g (6 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  4 -2 -6  4
Curve Equation t 840g1 [0,-1,0,-735,7920] 4 840g2 [0,-1,0,-740,7812] 8 840g3 [0,-1,0,-1720,-16100] 4 840g4 [0,-1,0,160,24732] 4 840g5 [0,-1,0,-24400,-1458548] 2 840g6 [0,-1,0,5280,-119700] 2
840h (4 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -4 -6 -2 -8
Curve Equation t Generators 840h1 [0,1,0,-71,-246] 2 [-5:3:1] 840h2 [0,1,0,-196,704] 4 [-10:42:1] 840h3 [0,1,0,-2896,59024] 2 [32:12:1] 840h4 [0,1,0,504,5184] 2 [0:72:1]
840i (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  0  2  2  4
Curve Equation t 840i1 [0,1,0,-36,-96] 2 840i2 [0,1,0,-56,0] 4 840i3 [0,1,0,-656,6240] 2 840i4 [0,1,0,224,224] 2
840j (6 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+  4 -2  2  4
Curve Equation t 840j1 [0,1,0,-15,90] 4 840j2 [0,1,0,-420,3168] 8 840j3 [0,1,0,-600,0] 4 840j4 [0,1,0,-6720,209808] 4 840j5 [0,1,0,-6480,-202272] 2 840j6 [0,1,0,2400,2400] 2

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