Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	1600g	Isogeny class
Conductor	1600	Conductor
∏ cp	8	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]
Generators	[253:3900:1]	Generators of the group modulo torsion
j	-20720464/15625	j-invariant
L	2.0075427510977	L(r)(E,1)/r!
Ω	0.29771528051174	Real period
R	3.3715816461401	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	1600r4 100a4 14400bf4 320c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600g4

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 1600g4

-4	8	-3	5	-7
1600r4	100a4	14400bf4	320c4	78400cb4

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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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