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	6006bf	Isogeny class
Conductor	6006	Conductor
∏ cp	960	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	1039667378061312 = 216 · 35 · 73 · 114 · 13	Discriminant
Eigenvalues	2- 3- -2 7- 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-32899,-1696447]	[a1,a2,a3,a4,a6]
Generators	[-124:755:1]	Generators of the group modulo torsion
j	3937972047511014577/1039667378061312	j-invariant
L	6.3451233385098	L(r)(E,1)/r!
Ω	0.36145282692232	Real period
R	0.073143746406883	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	48048bc1 18018k1 42042co1 66066x1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bf1

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	-	-	+	-2	-4	-4	-6	0	-10	-2	-4	0	-2	4	10	-8	16	-10	-8	8	-6	6

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Quadratic twists for elliptic curve 6006bf1

-4	-3	-7	-11	13
48048bc1	18018k1	42042co1	66066x1	78078z1

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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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