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	5166x	Isogeny class
Conductor	5166	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-15500913624 = -1 · 23 · 39 · 74 · 41	Discriminant
Eigenvalues	2- 3+ -1 7-  4 -3 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-758,-9827]	[a1,a2,a3,a4,a6]
Generators	[43:167:1]	Generators of the group modulo torsion
j	-2444008923/787528	j-invariant
L	5.5391273094737	L(r)(E,1)/r!
Ω	0.44763622485456	Real period
R	0.5155904692545	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41328o1 5166d1 129150d1 36162bt1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166x1

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
-	+	-1	-	4	-3	-3	-5	-4	-8	3	-8	+	10	0	-6	-1	-8	1	9	-11	-2	7	-7	-8

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Quadratic twists for elliptic curve 5166x1

-4	-3	5	-7
41328o1	5166d1	129150d1	36162bt1

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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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