Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Class	r	Atkin-Lehner	Eigenvalues
1600a (4 curves)	1	2+ 5+	2+  0 5+  4 -4 -2 -2 -4
Curve Equation t Generators 1600a1 [0,0,0,-200,1000] 2 [-15:25:1] 1600a2 [0,0,0,-700,-6000] 4 [-19:21:1] 1600a3 [0,0,0,-10700,-426000] 2 [13080:280700:27] 1600a4 [0,0,0,1300,-34000] 2 [110:1200:1]
1600b (1 curve)	1	2+ 5+	2+  1 5+  2 -5  0 -5 -5
Curve Equation t Generators 1600b1 [0,1,0,-33,-97] 1 [7:8:1]
1600c (4 curves)	1	2+ 5+	2+  1 5+ -2  3 -4  3 -5
Curve Equation t Generators 1600c1 [0,1,0,-193,1183] 1 [27:128:1] 1600c2 [0,1,0,1407,-8737] 1 [489:4096:27] 1600c3 [0,1,0,-833,-109537] 1 [59:224:1] 1600c4 [0,1,0,-200833,-34709537] 1 [31593:986048:27]
1600d (1 curve)	1	2+ 5+	2+ -1 5+ -2  5  0 -5  5
Curve Equation t Generators 1600d1 [0,-1,0,-33,97] 1 [1:8:1]
1600e (2 curves)	1	2+ 5+	2+  2 5+ -2 -4 -6 -2  8
Curve Equation t Generators 1600e1 [0,-1,0,-8,-238] 2 [187:2550:1] 1600e2 [0,-1,0,-633,-5863] 2 [32:75:1]
1600f (2 curves)	1	2+ 5+	2+ -2 5+  2  4 -6 -2 -8
Curve Equation t Generators 1600f1 [0,1,0,-8,238] 2 [13:50:1] 1600f2 [0,1,0,-633,5863] 2 [-7:100:1]
1600g (4 curves)	1	2+ 5+	2+ -2 5+ -2  0  2  6  4
Curve Equation t Generators 1600g1 [0,1,0,-133,363] 2 [-2:25:1] 1600g2 [0,1,0,367,2863] 2 [13:100:1] 1600g3 [0,1,0,-4133,-103637] 2 [143:1500:1] 1600g4 [0,1,0,-3633,-129137] 2 [253:3900:1]
1600h (1 curve)	1	2+ 5+	2+ -3 5+ -2 -1  4 -5 -1
Curve Equation t Generators 1600h1 [0,0,0,20,-80] 1 [6:16:1]
1600i (1 curve)	0	2+ 5-	2+  1 5-  2  5  0  5  5
Curve Equation t 1600i1 [0,1,0,-833,10463] 1
1600j (4 curves)	0	2+ 5-	2+ -1 5-  2  3  4 -3 -5
Curve Equation t 1600j1 [0,-1,0,-33,-863] 1 1600j2 [0,-1,0,-8033,-274463] 1 1600j3 [0,-1,0,-4833,157537] 1 1600j4 [0,-1,0,35167,-1162463] 1
1600k (1 curve)	0	2+ 5-	2+ -1 5- -2 -5  0  5 -5
Curve Equation t 1600k1 [0,-1,0,-833,-10463] 1
1600l (2 curves)	0	2+ 5-	2+  2 5- -2  4  4  0  4
Curve Equation t 1600l1 [0,-1,0,-13,-3] 2 1600l2 [0,-1,0,-113,497] 2
1600m (2 curves)	0	2+ 5-	2+ -2 5-  2  4 -4  0  4
Curve Equation t 1600m1 [0,1,0,-333,-1037] 2 1600m2 [0,1,0,-2833,56463] 2
1600n (1 curve)	0	2+ 5-	2+  3 5-  2 -1 -4  5 -1
Curve Equation t 1600n1 [0,0,0,500,-10000] 1
1600o (4 curves)	0	2- 5+	2-  0 5+  0  0  6 -2  0
Curve Equation t 1600o1 [0,0,0,25,0] 2 1600o2 [0,0,0,-100,0] 4 1600o3 [0,0,0,-1100,-14000] 2 1600o4 [0,0,0,-1100,14000] 2
1600p (4 curves)	0	2- 5+	2-  0 5+ -4  4 -2 -2  4
Curve Equation t 1600p1 [0,0,0,-200,-1000] 2 1600p2 [0,0,0,-700,6000] 4 1600p3 [0,0,0,-10700,426000] 2 1600p4 [0,0,0,1300,34000] 2
1600q (4 curves)	0	2- 5+	2- -1 5+  2 -3 -4  3  5
Curve Equation t 1600q1 [0,-1,0,-193,-1183] 1 1600q2 [0,-1,0,1407,8737] 1 1600q3 [0,-1,0,-833,109537] 1 1600q4 [0,-1,0,-200833,34709537] 1
1600r (4 curves)	0	2- 5+	2-  2 5+  2  0  2  6 -4
Curve Equation t 1600r1 [0,-1,0,-133,-363] 2 1600r2 [0,-1,0,367,-2863] 2 1600r3 [0,-1,0,-4133,103637] 2 1600r4 [0,-1,0,-3633,129137] 2
1600s (1 curve)	0	2- 5+	2-  3 5+  2  1  4 -5  1
Curve Equation t 1600s1 [0,0,0,20,80] 1
1600t (2 curves)	1	2- 5-	2-  0 5-  0  0  4 -8  0
Curve Equation t Generators 1600t1 [0,0,0,5,0] 2 [20:90:1] 1600t2 [0,0,0,-20,0] 2 [-4:4:1]
1600u (2 curves)	1	2- 5-	2-  0 5-  0  0 -4  8  0
Curve Equation t Generators 1600u1 [0,0,0,125,0] 2 [242:1419:8] 1600u2 [0,0,0,-500,0] 2 [-4:44:1]
1600v (4 curves)	1	2- 5-	2-  1 5- -2 -3  4 -3  5
Curve Equation t Generators 1600v1 [0,1,0,-33,863] 1 [7:32:1] 1600v2 [0,1,0,-8033,274463] 1 [23:320:1] 1600v3 [0,1,0,-4833,-157537] 1 [247:3712:1] 1600v4 [0,1,0,35167,1162463] 1 [2183:102400:1]
1600w (2 curves)	1	2- 5-	2-  2 5- -2 -4 -4  0 -4
Curve Equation t Generators 1600w1 [0,-1,0,-333,1037] 2 [-19:12:1] 1600w2 [0,-1,0,-2833,-56463] 2 [4467:298500:1]
1600x (2 curves)	1	2- 5-	2- -2 5-  2 -4  4  0 -4
Curve Equation t Generators 1600x1 [0,1,0,-13,3] 2 [-2:5:1] 1600x2 [0,1,0,-113,-497] 2 [-6:1:1]
1600y (1 curve)	1	2- 5-	2- -3 5- -2  1 -4  5  1
Curve Equation t Generators 1600y1 [0,0,0,500,10000] 1 [50:-400:1]

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