Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	1600a	Isogeny class
Conductor	1600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-640000000000 = -1 · 216 · 510	Discriminant
Eigenvalues	2+  0 5+  4 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1300,-34000]	[a1,a2,a3,a4,a6]
Generators	[110:1200:1]	Generators of the group modulo torsion
j	237276/625	j-invariant
L	2.9074905253085	L(r)(E,1)/r!
Ω	0.46941244031789	Real period
R	1.5484733017192	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1600p4 200c4 14400bp4 320b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600a4

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
+	0	+	4	-4	-2	-2	-4	-4	2	-8	6	-6	-8	-4	6	4	2	8	0	6	0	-16	-6	14

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Quadratic twists for elliptic curve 1600a4

-4	8	-3	5	-7
1600p4	200c4	14400bp4	320b4	78400w3

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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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