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	6600l	Isogeny class
Conductor	6600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-15468750000 = -1 · 24 · 32 · 510 · 11	Discriminant
Eigenvalues	2+ 3- 5+  4 11+ -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,617,1238]	[a1,a2,a3,a4,a6]
j	103737344/61875	j-invariant
L	3.0382798564345	L(r)(E,1)/r!
Ω	0.75956996410862	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200m1 52800bi1 19800bo1 1320i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600l1

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

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Quadratic twists for elliptic curve 6600l1

-4	8	-3	5	-11
13200m1	52800bi1	19800bo1	1320i1	72600eg1

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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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