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	5166y	Isogeny class
Conductor	5166	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	-2892298752 = -1 · 29 · 39 · 7 · 41	Discriminant
Eigenvalues	2- 3+  2 7- -5 -6  0  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-38504,2917675]	[a1,a2,a3,a4,a6]
Generators	[115:-31:1]	Generators of the group modulo torsion
j	-320729857537851/146944	j-invariant
L	6.0755986657357	L(r)(E,1)/r!
Ω	1.1664324271875	Real period
R	0.28937232139662	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	41328p1 5166e1 129150f1 36162bu1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166y1

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	-	-5	-6	0	1	-7	4	-9	4	+	-5	-3	-6	5	-5	-2	-6	10	-11	4	2	-17

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Quadratic twists for elliptic curve 5166y1

-4	-3	5	-7
41328p1	5166e1	129150f1	36162bu1

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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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