Cremona's table of elliptic curves

6608 = 2⁴ · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 7- 59+	Signs for the Atkin-Lehner involutions
Class	6608d	Isogeny class
Conductor	6608	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	5280	Modular degree for the optimal curve
Δ	-8123293696 = -1 · 213 · 75 · 59	Discriminant
Eigenvalues	2- -2 -3 7- -6 -2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,328,3796]	[a1,a2,a3,a4,a6]
Generators	[-2:56:1]	Generators of the group modulo torsion
j	949862087/1983226	j-invariant
L	1.8370815139067	L(r)(E,1)/r!
Ω	0.90804651168779	Real period
R	0.10115569468419	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	826a1 26432h1 59472bm1 46256bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6608d1

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	-3	-	-6	-2	4	-2	-3	6	-6	9	10	4	8	2	+	-10	-4	0	-10	-6	-9	-1	-1

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Quadratic twists for elliptic curve 6608d1

-4	8	-3	-7
826a1	26432h1	59472bm1	46256bm1

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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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