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	5166g	Isogeny class
Conductor	5166	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	69174145152 = 27 · 38 · 72 · 412	Discriminant
Eigenvalues	2+ 3-  0 7+ -2 -6  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-55242,-4983692]	[a1,a2,a3,a4,a6]
j	25574596275390625/94889088	j-invariant
L	0.62281911077145	L(r)(E,1)/r!
Ω	0.31140955538572	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	41328bu2 1722j2 129150dd2 36162z2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166g2

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	-6	2	-8	0	-4	4	-2	+	0	8	4	-2	8	-6	16	-14	8	10	14	2

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Quadratic twists for elliptic curve 5166g2

-4	-3	5	-7
41328bu2	1722j2	129150dd2	36162z2

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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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