Cremona's table of elliptic curves

6664 = 2³ · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17+	Signs for the Atkin-Lehner involutions
Class	6664c	Isogeny class
Conductor	6664	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	38304	Modular degree for the optimal curve
Δ	-2842216239794176 = -1 · 211 · 710 · 173	Discriminant
Eigenvalues	2-  0  1 7-  2  4 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-256907,50185702]	[a1,a2,a3,a4,a6]
Generators	[29058:1735063:8]	Generators of the group modulo torsion
j	-3241463778/4913	j-invariant
L	4.3289576778946	L(r)(E,1)/r!
Ω	0.4522371522442	Real period
R	9.5723176576989	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	13328c1 53312l1 59976q1 6664b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6664c1

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	1	-	2	4	+	-5	9	-6	-8	-11	4	-1	2	6	-9	-6	-7	1	-4	-8	4	15	0

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Quadratic twists for elliptic curve 6664c1

-4	8	-3	-7	17
13328c1	53312l1	59976q1	6664b1	113288u1

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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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