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	6006o	Isogeny class
Conductor	6006	Conductor
∏ cp	324	Product of Tamagawa factors cp
deg	829440	Modular degree for the optimal curve
Δ	1837810787484672 = 210 · 39 · 73 · 112 · 133	Discriminant
Eigenvalues	2+ 3-  0 7- 11+ 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-309011326,2090760854000]	[a1,a2,a3,a4,a6]
j	3263224124812796801735447265625/1837810787484672	j-invariant
L	1.81107112626	L(r)(E,1)/r!
Ω	0.20123012514	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	48048bj1 18018bs1 42042k1 66066cl1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006o1

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	8	-4	0	8	6	12	0	14	8	0	14	-16	6	-6	2

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Quadratic twists for elliptic curve 6006o1

-4	-3	-7	-11	13
48048bj1	18018bs1	42042k1	66066cl1	78078cw1

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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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