Cremona's table of elliptic curves

2400 = 2⁵ · 3 · 5²

Class	r	Atkin-Lehner	Eigenvalues
2400a (4 curves)	1	2+ 3+ 5+	2+ 3+ 5+  0  0 -2 -6  4
Curve Equation t Generators 2400a1 [0,-1,0,-258,1512] 4 [-13:50:1] 2400a2 [0,-1,0,-1008,-10488] 2 [-19:38:1] 2400a3 [0,-1,0,-4008,99012] 4 [137:1450:1] 2400a4 [0,-1,0,367,7137] 2 [7:100:1]
2400b (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+ -1  0 -1  0  3
Curve Equation t Generators 2400b1 [0,-1,0,-13,37] 1 [3:4:1]
2400c (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+  3  0 -5  0 -5
Curve Equation t Generators 2400c1 [0,-1,0,-733,-7403] 1 [51:292:1]
2400d (4 curves)	1	2+ 3+ 5+	2+ 3+ 5+ -4  0  2  6  0
Curve Equation t Generators 2400d1 [0,-1,0,-758,-7488] 4 [-17:14:1] 2400d2 [0,-1,0,-12008,-502488] 2 [1946:26425:8] 2400d3 [0,-1,0,-2008,25012] 2 [-44:162:1] 2400d4 [0,-1,0,367,-28863] 2 [47:300:1]
2400e (2 curves)	0	2+ 3+ 5-	2+ 3+ 5- -2  6 -2 -6 -4
Curve Equation t 2400e1 [0,-1,0,42,912] 2 2400e2 [0,-1,0,-1208,15912] 2
2400f (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  3  0  5  0  5
Curve Equation t 2400f1 [0,-1,0,-18333,962037] 1
2400g (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  3 -4 -7  4  1
Curve Equation t 2400g1 [0,-1,0,-4333,-815963] 1
2400h (2 curves)	0	2+ 3+ 5-	2+ 3+ 5-  4  0  4  0  8
Curve Equation t 2400h1 [0,-1,0,-538,-4628] 2 2400h2 [0,-1,0,-513,-5103] 2
2400i (1 curve)	0	2+ 3- 5+	2+ 3- 5+  1  0 -1  0 -3
Curve Equation t 2400i1 [0,1,0,-13,-37] 1
2400j (1 curve)	0	2+ 3- 5+	2+ 3- 5+  1  4  3  4  1
Curve Equation t 2400j1 [0,1,0,1667,-42037] 1
2400k (4 curves)	0	2+ 3- 5+	2+ 3- 5+  4  0  2  6  0
Curve Equation t 2400k1 [0,1,0,-758,7488] 4 2400k2 [0,1,0,-2008,-25012] 2 2400k3 [0,1,0,-12008,502488] 2 2400k4 [0,1,0,367,28863] 2
2400l (4 curves)	0	2+ 3- 5+	2+ 3- 5+  4  4 -6 -2  4
Curve Equation t 2400l1 [0,1,0,-5658,158688] 4 2400l2 [0,1,0,-12408,-300312] 2 2400l3 [0,1,0,-90033,10368063] 2 2400l4 [0,1,0,592,496188] 2
2400m (4 curves)	0	2+ 3- 5+	2+ 3- 5+ -4 -4  2  6  4
Curve Equation t 2400m1 [0,1,0,-58,-112] 4 2400m2 [0,1,0,-808,-9112] 2 2400m3 [0,1,0,-433,3263] 2 2400m4 [0,1,0,192,-612] 2
2400n (1 curve)	1	2+ 3- 5-	2+ 3- 5-  1 -4 -3 -4 -1
Curve Equation t Generators 2400n1 [0,1,0,67,363] 1 [13:-60:1]
2400o (2 curves)	1	2+ 3- 5-	2+ 3- 5-  2 -6 -2 -6  4
Curve Equation t Generators 2400o1 [0,1,0,42,-912] 2 [89:846:1] 2400o2 [0,1,0,-1208,-15912] 2 [-18:18:1]
2400p (1 curve)	1	2+ 3- 5-	2+ 3- 5- -3  4 -7  4 -1
Curve Equation t Generators 2400p1 [0,1,0,-4333,815963] 1 [-67:900:1]
2400q (2 curves)	1	2+ 3- 5-	2+ 3- 5- -4  0  4  0 -8
Curve Equation t Generators 2400q1 [0,1,0,-538,4628] 2 [8:30:1] 2400q2 [0,1,0,-513,5103] 2 [3:60:1]
2400r (4 curves)	0	2- 3+ 5+	2- 3+ 5+  0  4 -2  2  8
Curve Equation t 2400r1 [0,-1,0,-158,312] 4 2400r2 [0,-1,0,-1408,-19688] 2 2400r3 [0,-1,0,-2033,35937] 4 2400r4 [0,-1,0,592,1812] 2
2400s (1 curve)	0	2- 3+ 5+	2- 3+ 5+ -1 -4  3  4 -1
Curve Equation t 2400s1 [0,-1,0,1667,42037] 1
2400t (1 curve)	0	2- 3+ 5+	2- 3+ 5+  3  4  7 -4 -1
Curve Equation t 2400t1 [0,-1,0,-173,6597] 1
2400u (4 curves)	0	2- 3+ 5+	2- 3+ 5+  4  4  2  6 -4
Curve Equation t 2400u1 [0,-1,0,-58,112] 4 2400u2 [0,-1,0,-433,-3263] 2 2400u3 [0,-1,0,-808,9112] 2 2400u4 [0,-1,0,192,612] 2
2400v (4 curves)	0	2- 3+ 5+	2- 3+ 5+ -4 -4 -6 -2 -4
Curve Equation t 2400v1 [0,-1,0,-5658,-158688] 4 2400v2 [0,-1,0,-90033,-10368063] 2 2400v3 [0,-1,0,-12408,300312] 2 2400v4 [0,-1,0,592,-496188] 2
2400w (1 curve)	1	2- 3+ 5-	2- 3+ 5- -1  0  1  0 -3
Curve Equation t Generators 2400w1 [0,-1,0,-333,-3963] 1 [23:4:1]
2400x (1 curve)	1	2- 3+ 5-	2- 3+ 5- -1  4 -3 -4  1
Curve Equation t Generators 2400x1 [0,-1,0,67,-363] 1 [7:20:1]
2400y (2 curves)	1	2- 3+ 5-	2- 3+ 5- -2 -6  2  6  4
Curve Equation t Generators 2400y1 [0,-1,0,2,-8] 2 [3:4:1] 2400y2 [0,-1,0,-48,-108] 2 [-4:2:1]
2400z (2 curves)	1	2- 3+ 5-	2- 3+ 5-  4  0 -4  0 -8
Curve Equation t Generators 2400z1 [0,-1,0,-13458,605412] 2 [66:18:1] 2400z2 [0,-1,0,-12833,663537] 2 [-8:875:1]
2400ba (4 curves)	1	2- 3- 5+	2- 3- 5+  0  0 -2 -6 -4
Curve Equation t Generators 2400ba1 [0,1,0,-258,-1512] 4 [42:252:1] 2400ba2 [0,1,0,-4008,-99012] 2 [586:609:8] 2400ba3 [0,1,0,-1008,10488] 2 [-22:150:1] 2400ba4 [0,1,0,367,-7137] 4 [18:75:1]
2400bb (4 curves)	1	2- 3- 5+	2- 3- 5+  0 -4 -2  2 -8
Curve Equation t Generators 2400bb1 [0,1,0,-158,-312] 4 [-3:12:1] 2400bb2 [0,1,0,-2033,-35937] 2 [63:300:1] 2400bb3 [0,1,0,-1408,19688] 4 [-37:150:1] 2400bb4 [0,1,0,592,-1812] 2 [147:1812:1]
2400bc (1 curve)	1	2- 3- 5+	2- 3- 5+ -3  0 -5  0  5
Curve Equation t Generators 2400bc1 [0,1,0,-733,7403] 1 [17:12:1]
2400bd (1 curve)	1	2- 3- 5+	2- 3- 5+ -3 -4  7 -4  1
Curve Equation t Generators 2400bd1 [0,1,0,-173,-6597] 1 [49:324:1]
2400be (1 curve)	0	2- 3- 5-	2- 3- 5-  1  0  1  0  3
Curve Equation t 2400be1 [0,1,0,-333,3963] 1
2400bf (2 curves)	0	2- 3- 5-	2- 3- 5-  2  6  2  6 -4
Curve Equation t 2400bf1 [0,1,0,2,8] 2 2400bf2 [0,1,0,-48,108] 2
2400bg (1 curve)	0	2- 3- 5-	2- 3- 5- -3  0  5  0 -5
Curve Equation t 2400bg1 [0,1,0,-18333,-962037] 1
2400bh (2 curves)	0	2- 3- 5-	2- 3- 5- -4  0 -4  0  8
Curve Equation t 2400bh1 [0,1,0,-13458,-605412] 2 2400bh2 [0,1,0,-12833,-663537] 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