Cremona's table of elliptic curves

5166 = 2 · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	5166j	Isogeny class
Conductor	5166	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	89028205656642 = 2 · 38 · 74 · 414	Discriminant
Eigenvalues	2+ 3- -2 7+  0  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-16308,-656586]	[a1,a2,a3,a4,a6]
j	657980877056833/122123738898	j-invariant
L	0.85577688959088	L(r)(E,1)/r!
Ω	0.42788844479544	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41328ca3 1722o3 129150da3 36162bf3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166j4

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
+	-	-2	+	0	6	-2	-4	0	-2	-8	6	+	4	8	6	0	10	8	-8	-6	-16	0	-10	2

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Quadratic twists for elliptic curve 5166j4

-4	-3	5	-7
41328ca3	1722o3	129150da3	36162bf3

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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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