Cremona's table of elliptic curves

630 = 2 · 3² · 5 · 7

Class	r	Atkin-Lehner	Eigenvalues
630a (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0  2  0  2
Curve Equation t 630a1 [1,-1,0,-105,441] 6 630a2 [1,-1,0,-75,675] 6 630a3 [1,-1,0,-420,-2800] 2 630a4 [1,-1,0,660,-15544] 2
630b (2 curves)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+ -4  6  4  6
Curve Equation t 630b1 [1,-1,0,-5124,142160] 2 630b2 [1,-1,0,-3204,248528] 2
630c (8 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  4 -2 -2  4
Curve Equation t 630c1 [1,-1,0,1890,-24300] 2 630c2 [1,-1,0,-9630,-210924] 4 630c3 [1,-1,0,-135630,-19186524] 2 630c4 [1,-1,0,-67950,6682500] 4 630c5 [1,-1,0,-1080450,432540000] 4 630c6 [1,-1,0,11430,21304296] 2 630c7 [1,-1,0,-17287200,27669604050] 2 630c8 [1,-1,0,-1073700,438205950] 2
630d (6 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7- -4 -2 -2 -4
Curve Equation t Generators 630d1 [1,-1,0,90,436] 2 [5:29:1] 630d2 [1,-1,0,-630,4900] 4 [-7:98:1] 630d3 [1,-1,0,-3330,-69080] 2 [-34:80:1] 630d4 [1,-1,0,-9450,355936] 4 [38:206:1] 630d5 [1,-1,0,-151200,22667386] 2 [225:-106:1] 630d6 [1,-1,0,-8820,404950] 2 [45:290:1]
630e (4 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -4 -6 -2  0
Curve Equation t Generators 630e1 [1,-1,0,21,53] 2 [2:9:1] 630e2 [1,-1,0,-159,665] 4 [-4:37:1] 630e3 [1,-1,0,-789,-7777] 2 [-13:19:1] 630e4 [1,-1,0,-2409,46115] 2 [31:7:1]
630f (8 curves)	0	2+ 3- 5- 7-	2+ 3- 5- 7-  0  2  6 -4
Curve Equation t 630f1 [1,-1,0,-369,1053] 2 630f2 [1,-1,0,-3249,-69795] 4 630f3 [1,-1,0,-24129,1448685] 6 630f4 [1,-1,0,-51849,-4531275] 2 630f5 [1,-1,0,-729,-177147] 2 630f6 [1,-1,0,-24309,1426113] 12 630f7 [1,-1,0,-58059,-3373137] 6 630f8 [1,-1,0,6561,4778595] 6
630g (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  4  6 -4  6
Curve Equation t 630g1 [1,-1,1,-46118,-3792203] 2 630g2 [1,-1,1,-28838,-6681419] 2
630h (4 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  0  2  0  2
Curve Equation t 630h1 [1,-1,1,-47,119] 6 630h2 [1,-1,1,73,551] 6 630h3 [1,-1,1,-947,-10961] 2 630h4 [1,-1,1,-677,-17549] 2
630i (8 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  0  2  6  8
Curve Equation t 630i1 [1,-1,1,-4478,-114163] 2 630i2 [1,-1,1,-5198,-74419] 4 630i3 [1,-1,1,-13253,449597] 6 630i4 [1,-1,1,-39218,2946557] 2 630i5 [1,-1,1,17302,-560419] 2 630i6 [1,-1,1,-197573,33848381] 12 630i7 [1,-1,1,-3161093,2164026557] 6 630i8 [1,-1,1,-183173,38980541] 6
630j (4 curves)	0	2- 3- 5- 7+	2- 3- 5- 7+  4 -2  6  0
Curve Equation t 630j1 [1,-1,1,-32,51] 4 630j2 [1,-1,1,-212,-1101] 4 630j3 [1,-1,1,-3362,-74181] 2 630j4 [1,-1,1,58,-3909] 2

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

Part of Computational Number Theory
Back to Tables and computations