Cremona's table of elliptic curves

1040 = 2⁴ · 5 · 13

Class	r	Atkin-Lehner	Eigenvalues
1040a (4 curves)	1	2+ 5+ 13+	2+  0 5+  0  4 13+ -6 -4
Curve Equation t Generators 1040a1 [0,0,0,-23,-42] 2 [6:6:1] 1040a2 [0,0,0,-43,42] 4 [-3:12:1] 1040a3 [0,0,0,-563,5138] 2 [-11:100:1] 1040a4 [0,0,0,157,322] 2 [7:42:1]
1040b (2 curves)	1	2+ 5- 13-	2+ -2 5-  0 -2 13-  2 -2
Curve Equation t Generators 1040b1 [0,1,0,-20,28] 2 [-2:8:1] 1040b2 [0,1,0,0,100] 2 [0:10:1]
1040c (2 curves)	0	2- 5+ 13+	2-  2 5+  4 -2 13+  2  6
Curve Equation t 1040c1 [0,-1,0,-16,0] 2 1040c2 [0,-1,0,64,-64] 2
1040d (2 curves)	0	2- 5+ 13+	2- -2 5+ -2 -4 13+  2  0
Curve Equation t 1040d1 [0,1,0,-281,-1910] 2 1040d2 [0,1,0,-276,-1976] 2
1040e (2 curves)	0	2- 5+ 13+	2- -2 5+  4  2 13+  2 -6
Curve Equation t 1040e1 [0,1,0,-13456,596244] 2 1040e2 [0,1,0,-12176,715540] 2
1040f (4 curves)	0	2- 5- 13-	2-  0 5-  0  0 13-  2  8
Curve Equation t 1040f1 [0,0,0,-107,154] 2 1040f2 [0,0,0,-1387,19866] 4 1040f3 [0,0,0,-22187,1272026] 4 1040f4 [0,0,0,-1067,29274] 4
1040g (4 curves)	0	2- 5- 13-	2-  2 5-  4  6 13- -6 -2
Curve Equation t 1040g1 [0,-1,0,-520,-4368] 2 1040g2 [0,-1,0,-200,-10000] 2 1040g3 [0,-1,0,-3320,71792] 2 1040g4 [0,-1,0,1800,268400] 2

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

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