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	5166v	Isogeny class
Conductor	5166	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-22596084 = -1 · 22 · 39 · 7 · 41	Discriminant
Eigenvalues	2- 3+ -1 7+  0 -1  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,52,163]	[a1,a2,a3,a4,a6]
Generators	[13:47:1]	Generators of the group modulo torsion
j	804357/1148	j-invariant
L	5.2393759766801	L(r)(E,1)/r!
Ω	1.4497956352448	Real period
R	0.90346802151107	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	41328bb1 5166b1 129150h1 36162bo1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166v1

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	+	0	-1	4	0	-5	-5	-4	7	-	-2	-3	3	-4	-6	-13	6	2	-11	-14	-4	-7

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Quadratic twists for elliptic curve 5166v1

-4	-3	5	-7
41328bb1	5166b1	129150h1	36162bo1

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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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