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	6600d	Isogeny class
Conductor	6600	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	73920	Modular degree for the optimal curve
Δ	-88373603357107200 = -1 · 210 · 311 · 52 · 117	Discriminant
Eigenvalues	2+ 3+ 5+ -3 11+ -4  1  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-768888,260153532]	[a1,a2,a3,a4,a6]
Generators	[506:628:1]	Generators of the group modulo torsion
j	-1963692857508260740/3452093881137	j-invariant
L	2.9644793200552	L(r)(E,1)/r!
Ω	0.34002532236245	Real period
R	4.3592037490889	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	13200ba1 52800df1 19800bn1 6600bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600d1

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

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Quadratic twists for elliptic curve 6600d1

-4	8	-3	5	-11
13200ba1	52800df1	19800bn1	6600bf1	72600cu1

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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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