Cremona's table of elliptic curves

624 = 2⁴ · 3 · 13

Class	r	Atkin-Lehner	Eigenvalues
624a (2 curves)	1	2+ 3+ 13+	2+ 3+  0  0 -6 13+  2  0
Curve Equation t Generators 624a1 [0,-1,0,-3,6] 2 [2:2:1] 624a2 [0,-1,0,-68,240] 2 [4:4:1]
624b (2 curves)	1	2+ 3+ 13+	2+ 3+ -4  4  2 13+ -6 -4
Curve Equation t Generators 624b1 [0,-1,0,5,-14] 2 [6:14:1] 624b2 [0,-1,0,-60,-144] 2 [-4:4:1]
624c (4 curves)	0	2+ 3+ 13-	2+ 3+  2  0  0 13-  2  4
Curve Equation t 624c1 [0,-1,0,-7,-2] 2 624c2 [0,-1,0,-52,160] 4 624c3 [0,-1,0,-832,9520] 2 624c4 [0,-1,0,8,448] 4
624d (2 curves)	0	2+ 3- 13+	2+ 3-  0  4  2 13+ -6  4
Curve Equation t 624d1 [0,1,0,-3,0] 2 624d2 [0,1,0,12,12] 2
624e (2 curves)	0	2+ 3- 13+	2+ 3-  4  0  2 13+  2 -8
Curve Equation t 624e1 [0,1,0,-651,-6228] 2 624e2 [0,1,0,564,-25668] 2
624f (4 curves)	1	2+ 3- 13-	2+ 3- -2 -4  0 13-  2 -8
Curve Equation t Generators 624f1 [0,1,0,-39,-108] 2 [12:36:1] 624f2 [0,1,0,-44,-84] 4 [-5:6:1] 624f3 [0,1,0,-304,1892] 4 [-16:54:1] 624f4 [0,1,0,136,-444] 4 [7:30:1]
624g (4 curves)	1	2- 3+ 13-	2- 3+  0 -2  0 13- -6 -2
Curve Equation t Generators 624g1 [0,-1,0,-13,4] 2 [0:2:1] 624g2 [0,-1,0,-148,-644] 2 [45:286:1] 624g3 [0,-1,0,-733,7888] 2 [12:26:1] 624g4 [0,-1,0,-748,7564] 2 [21:26:1]
624h (4 curves)	0	2- 3- 13-	2- 3-  2  4 -4 13-  2  0
Curve Equation t 624h1 [0,1,0,8,20] 2 624h2 [0,1,0,-72,180] 4 624h3 [0,1,0,-312,-2028] 2 624h4 [0,1,0,-1112,13908] 4
624i (4 curves)	0	2- 3- 13-	2- 3-  2 -4  4 13-  2  8
Curve Equation t 624i1 [0,1,0,-312,-44460] 2 624i2 [0,1,0,-20792,-1150380] 4 624i3 [0,1,0,-331832,-73684908] 2 624i4 [0,1,0,-37432,932948] 4
624j (2 curves)	0	2- 3- 13-	2- 3- -4  2  4 13-  2  2
Curve Equation t 624j1 [0,1,0,-5,-6] 2 624j2 [0,1,0,-20,24] 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