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	6600k	Isogeny class
Conductor	6600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	10560	Modular degree for the optimal curve
Δ	-907500000000 = -1 · 28 · 3 · 510 · 112	Discriminant
Eigenvalues	2+ 3- 5+  3 11+  5 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-833,-47037]	[a1,a2,a3,a4,a6]
j	-25600/363	j-invariant
L	3.0309687579165	L(r)(E,1)/r!
Ω	0.37887109473956	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13200k1 52800bg1 19800bm1 6600x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600k1

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	+	5	-6	-1	-6	6	-5	6	10	7	-4	-2	12	9	13	0	2	12	2	-6	-1

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Quadratic twists for elliptic curve 6600k1

-4	8	-3	5	-11
13200k1	52800bg1	19800bm1	6600x1	72600dz1

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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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