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	36	Product of Tamagawa factors cp
Δ	71708514189312 = 218 · 3 · 73 · 112 · 133	Discriminant
Eigenvalues	2+ 3-  0 7- 11- 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-48976,-4155874]	[a1,a2,a3,a4,a6]
Generators	[-126:199:1]	Generators of the group modulo torsion
j	12991547986467765625/71708514189312	j-invariant
L	3.7537276772843	L(r)(E,1)/r!
Ω	0.32103259010432	Real period
R	1.2991853970217	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	48048bd3 18018bn3 42042q3 66066ck3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006q3

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 6006q3

-4	-3	-7	-11	13
48048bd3	18018bn3	42042q3	66066ck3	78078cs3

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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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