Cremona's table of elliptic curves

6006 = 2 · 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	6006be	Isogeny class
Conductor	6006	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-2131024896 = -1 · 210 · 33 · 72 · 112 · 13	Discriminant
Eigenvalues	2- 3- -2 7- 11+ 13-  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,241,-1671]	[a1,a2,a3,a4,a6]
Generators	[10:37:1]	Generators of the group modulo torsion
j	1547612421263/2131024896	j-invariant
L	6.3121197793966	L(r)(E,1)/r!
Ω	0.78008678229295	Real period
R	0.26971869979402	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	48048bn1 18018q1 42042bz1 66066u1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006be1

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	-6	-6	2	-10	4	-2	-8	4	-8	4	2	-8	4	16	-16	-8	-2	2

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Quadratic twists for elliptic curve 6006be1

-4	-3	-7	-11	13
48048bn1	18018q1	42042bz1	66066u1	78078bh1

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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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