Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Class	1600r	Isogeny class
Conductor	1600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4000000000000 = -1 · 214 · 512	Discriminant
Eigenvalues	2-  2 5+  2  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3633,129137]	[a1,a2,a3,a4,a6]
j	-20720464/15625	j-invariant
L	2.876616721784	L(r)(E,1)/r!
Ω	0.719154180446	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1600g4 400e4 14400dw4 320f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600r4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	2	+	2	0	2	6	-4	6	-6	4	2	6	10	-6	-6	12	-2	-2	12	-2	-8	-6	-6	-2

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Quadratic twists for elliptic curve 1600r4

-4	8	-3	5	-7
1600g4	400e4	14400dw4	320f4	78400ik4

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

Part of Computational Number Theory
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