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	6600w	Isogeny class
Conductor	6600	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-54579318750000 = -1 · 24 · 38 · 58 · 113	Discriminant
Eigenvalues	2- 3+ 5+  2 11-  0  8 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7717,238812]	[a1,a2,a3,a4,a6]
Generators	[53:891:1]	Generators of the group modulo torsion
j	203269830656/218317275	j-invariant
L	3.7796747040438	L(r)(E,1)/r!
Ω	0.41713988081373	Real period
R	0.75507738888265	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	13200s1 52800cc1 19800e1 1320d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600w1

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

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Quadratic twists for elliptic curve 6600w1

-4	8	-3	5	-11
13200s1	52800cc1	19800e1	1320d1	72600l1

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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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