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	8664d	Isogeny class
Conductor	8664	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	16416	Modular degree for the optimal curve
Δ	-7336899233712 = -1 · 24 · 33 · 198	Discriminant
Eigenvalues	2+ 3-  0  3  2  1  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22863,-1344618]	[a1,a2,a3,a4,a6]
j	-4864000/27	j-invariant
L	3.4931162323438	L(r)(E,1)/r!
Ω	0.19406201290799	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17328a1 69312a1 25992u1 8664h1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 8664d1

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	3	2	1	4	+	-4	0	7	-1	4	1	-2	12	-2	-1	13	10	-3	-13	-8	18	2

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Quadratic twists for elliptic curve 8664d1

-4	8	-3	-19
17328a1	69312a1	25992u1	8664h1

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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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