Cremona's table of elliptic curves

8664 = 2³ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 19-	Signs for the Atkin-Lehner involutions
Class	8664o	Isogeny class
Conductor	8664	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	28800	Modular degree for the optimal curve
Δ	2745973982208 = 210 · 3 · 197	Discriminant
Eigenvalues	2- 3-  4  4 -4  4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5896,-156928]	[a1,a2,a3,a4,a6]
j	470596/57	j-invariant
L	4.9422773465031	L(r)(E,1)/r!
Ω	0.54914192738924	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17328h1 69312ba1 25992p1 456a1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664o1

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
-	-	4	4	-4	4	6	-	-6	-2	-2	-4	6	4	-2	6	4	-10	-8	0	-2	-14	-16	18	-14

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Quadratic twists for elliptic curve 8664o1

-4	8	-3	-19
17328h1	69312ba1	25992p1	456a1

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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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