Cremona's table of elliptic curves

9009 = 3² · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	9009d	Isogeny class
Conductor	9009	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	14428931517 = 38 · 7 · 11 · 134	Discriminant
Eigenvalues	-1 3- -2 7+ 11+ 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-33296,-2330130]	[a1,a2,a3,a4,a6]
Generators	[-105:54:1] [951:28254:1]	Generators of the group modulo torsion
j	5599640476399033/19792773	j-invariant
L	3.5061573806272	L(r)(E,1)/r!
Ω	0.35342938100622	Real period
R	9.9203902365037	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3003a4 63063p4 99099cb4 117117bq4	Quadratic twists by: -3 -7 -11 13

Hecke Eigenvalues for elliptic curve 9009d3

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
-1	-	-2	+	+	+	-6	-4	0	-6	-4	-2	-6	0	-4	-6	8	10	-4	-8	6	4	-12	2	-10

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Quadratic twists for elliptic curve 9009d3

-3	-7	-11	13
3003a4	63063p4	99099cb4	117117bq4

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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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