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	5166bk	Isogeny class
Conductor	5166	Conductor
∏ cp	112	Product of Tamagawa factors cp
Δ	376614790272 = 27 · 36 · 74 · 412	Discriminant
Eigenvalues	2- 3- -2 7-  2  4 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6521,202137]	[a1,a2,a3,a4,a6]
Generators	[-21:584:1]	Generators of the group modulo torsion
j	42060685455433/516618368	j-invariant
L	5.288848750691	L(r)(E,1)/r!
Ω	0.95603694303619	Real period
R	0.19757338537772	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	41328bp2 574c2 129150t2 36162cm2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166bk2

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	-	2	4	-6	-6	-8	4	-8	10	-	-4	-8	8	4	-10	-2	-12	10	0	0	-18	-10

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Quadratic twists for elliptic curve 5166bk2

-4	-3	5	-7
41328bp2	574c2	129150t2	36162cm2

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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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