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	6600bc	Isogeny class
Conductor	6600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	41250000 = 24 · 3 · 57 · 11	Discriminant
Eigenvalues	2- 3- 5+  0 11-  6  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1383,-20262]	[a1,a2,a3,a4,a6]
j	1171019776/165	j-invariant
L	3.1313492412055	L(r)(E,1)/r!
Ω	0.78283731030138	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200b1 52800h1 19800d1 1320b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600bc1

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

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Quadratic twists for elliptic curve 6600bc1

-4	8	-3	5	-11
13200b1	52800h1	19800d1	1320b1	72600bk1

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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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