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	8664b	Isogeny class
Conductor	8664	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	54720	Modular degree for the optimal curve
Δ	-1056513489654528 = -1 · 28 · 35 · 198	Discriminant
Eigenvalues	2+ 3+ -2 -5 -4  5  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16004,-1741932]	[a1,a2,a3,a4,a6]
Generators	[241:2888:1]	Generators of the group modulo torsion
j	-104272/243	j-invariant
L	2.226183388563	L(r)(E,1)/r!
Ω	0.19824191545995	Real period
R	1.8716050230833	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	17328j1 69312bg1 25992w1 8664n1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664b1

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	-5	-4	5	0	+	-6	8	-1	7	0	-11	10	6	8	-1	5	6	1	-13	-4	-12	2

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Quadratic twists for elliptic curve 8664b1

-4	8	-3	-19
17328j1	69312bg1	25992w1	8664n1

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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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