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	6006q	Isogeny class
Conductor	6006	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	28784156647454208 = 29 · 32 · 76 · 11 · 136	Discriminant
Eigenvalues	2+ 3-  0 7- 11- 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-77136,1160734]	[a1,a2,a3,a4,a6]
Generators	[-208:2970:1]	Generators of the group modulo torsion
j	50755950018496437625/28784156647454208	j-invariant
L	3.7537276772843	L(r)(E,1)/r!
Ω	0.32103259010432	Real period
R	0.64959269851084	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	48048bd4 18018bn4 42042q4 66066ck4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006q4

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	-	-	-	6	-4	-6	-6	-4	-4	0	-4	-6	-12	-12	-10	-4	12	-10	8	6	18	14

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Quadratic twists for elliptic curve 6006q4

-4	-3	-7	-11	13
48048bd4	18018bn4	42042q4	66066ck4	78078cs4

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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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