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	6006y	Isogeny class
Conductor	6006	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	208773754353496332 = 22 · 35 · 72 · 1110 · 132	Discriminant
Eigenvalues	2- 3+  0 7- 11- 13-  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-210398,-30030001]	[a1,a2,a3,a4,a6]
Generators	[-199:2101:1]	Generators of the group modulo torsion
j	1030027127420340582625/208773754353496332	j-invariant
L	5.2260165715955	L(r)(E,1)/r!
Ω	0.22608369635938	Real period
R	1.1557703310212	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	48048cd2 18018l2 42042dh2 66066d2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006y2

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

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Quadratic twists for elliptic curve 6006y2

-4	-3	-7	-11	13
48048cd2	18018l2	42042dh2	66066d2	78078a2

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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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