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	160	Product of Tamagawa factors cp
deg	38400	Modular degree for the optimal curve
Δ	-4749320388404592 = -1 · 24 · 310 · 74 · 115 · 13	Discriminant
Eigenvalues	2- 3+  0 7- 11- 13-  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,27742,-2786785]	[a1,a2,a3,a4,a6]
Generators	[95:799:1]	Generators of the group modulo torsion
j	2361217731530033375/4749320388404592	j-invariant
L	5.2260165715955	L(r)(E,1)/r!
Ω	0.22608369635938	Real period
R	0.57788516551059	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	48048cd1 18018l1 42042dh1 66066d1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006y1

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 6006y1

-4	-3	-7	-11	13
48048cd1	18018l1	42042dh1	66066d1	78078a1

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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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