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	6664a	Isogeny class
Conductor	6664	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-29002206528512 = -1 · 210 · 78 · 173	Discriminant
Eigenvalues	2- -3  2 7+  5 -7 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4459,283318]	[a1,a2,a3,a4,a6]
j	-1660932/4913	j-invariant
L	1.1673753755039	L(r)(E,1)/r!
Ω	0.58368768775193	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	13328a1 53312g1 59976i1 6664f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6664a1

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
-	-3	2	+	5	-7	+	2	0	6	-4	-8	2	8	10	-3	0	12	2	1	-2	13	-4	-15	0

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Quadratic twists for elliptic curve 6664a1

-4	8	-3	-7	17
13328a1	53312g1	59976i1	6664f1	113288s1

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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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