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	5166bc	Isogeny class
Conductor	5166	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	226063027860768 = 25 · 36 · 78 · 412	Discriminant
Eigenvalues	2- 3-  2 7+  6 -4  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-19994,-807879]	[a1,a2,a3,a4,a6]
j	1212480836738137/310100175392	j-invariant
L	4.0906724553456	L(r)(E,1)/r!
Ω	0.40906724553456	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41328cj2 574b2 129150bp2 36162cq2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166bc2

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	+	6	-4	2	2	0	0	0	10	-	4	-8	4	8	10	-14	12	-6	0	-4	14	-10

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Quadratic twists for elliptic curve 5166bc2

-4	-3	5	-7
41328cj2	574b2	129150bp2	36162cq2

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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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