Cremona's table of elliptic curves

6600 = 2³ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 11+	Signs for the Atkin-Lehner involutions
Class	6600x	Isogeny class
Conductor	6600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-58080000 = -1 · 28 · 3 · 54 · 112	Discriminant
Eigenvalues	2- 3+ 5- -3 11+ -5  6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,-363]	[a1,a2,a3,a4,a6]
Generators	[11:22:1]	Generators of the group modulo torsion
j	-25600/363	j-invariant
L	2.9532616636747	L(r)(E,1)/r!
Ω	0.84718152254743	Real period
R	0.87149612718014	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	13200bf1 52800dy1 19800w1 6600k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600x1

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	+	-5	6	-1	6	6	-5	-6	10	-7	4	2	12	9	-13	0	-2	12	-2	-6	1

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Quadratic twists for elliptic curve 6600x1

-4	8	-3	5	-11
13200bf1	52800dy1	19800w1	6600k1	72600x1

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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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