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	6006t	Isogeny class
Conductor	6006	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	3435432 = 23 · 3 · 7 · 112 · 132	Discriminant
Eigenvalues	2- 3+  0 7- 11+ 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-893,9899]	[a1,a2,a3,a4,a6]
Generators	[-19:152:1]	Generators of the group modulo torsion
j	78760503564625/3435432	j-invariant
L	5.1424104430551	L(r)(E,1)/r!
Ω	2.3556859907876	Real period
R	0.72765929799438	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	48048cg2 18018n2 42042de2 66066j2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006t2

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

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Quadratic twists for elliptic curve 6006t2

-4	-3	-7	-11	13
48048cg2	18018n2	42042de2	66066j2	78078e2

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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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