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	56	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	23995367424 = 214 · 36 · 72 · 41	Discriminant
Eigenvalues	2- 3- -2 7-  2  4 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-761,-2919]	[a1,a2,a3,a4,a6]
Generators	[-9:60:1]	Generators of the group modulo torsion
j	66775173193/32915456	j-invariant
L	5.288848750691	L(r)(E,1)/r!
Ω	0.95603694303619	Real period
R	0.39514677075543	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	41328bp1 574c1 129150t1 36162cm1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166bk1

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 5166bk1

-4	-3	5	-7
41328bp1	574c1	129150t1	36162cm1

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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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