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	6600c	Isogeny class
Conductor	6600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	12251250000 = 24 · 34 · 57 · 112	Discriminant
Eigenvalues	2+ 3+ 5+  2 11+  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3283,73312]	[a1,a2,a3,a4,a6]
Generators	[7:225:1]	Generators of the group modulo torsion
j	15657723904/49005	j-invariant
L	3.7459659320123	L(r)(E,1)/r!
Ω	1.2722584409239	Real period
R	0.73608588701761	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200z1 52800da1 19800bk1 1320k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600c1

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

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Quadratic twists for elliptic curve 6600c1

-4	8	-3	5	-11
13200z1	52800da1	19800bk1	1320k1	72600cs1

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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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