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	5166be	Isogeny class
Conductor	5166	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-50657416304166 = -1 · 2 · 37 · 710 · 41	Discriminant
Eigenvalues	2- 3- -3 7+  4  1 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1139,-342471]	[a1,a2,a3,a4,a6]
j	-223980311017/69488911254	j-invariant
L	2.2674472550364	L(r)(E,1)/r!
Ω	0.28343090687955	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41328cm1 1722a1 129150bm1 36162cr1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5166be1

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
-	-	-3	+	4	1	-3	-3	6	8	-1	-8	-	-6	-8	-4	3	4	1	9	3	16	11	1	8

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Quadratic twists for elliptic curve 5166be1

-4	-3	5	-7
41328cm1	1722a1	129150bm1	36162cr1

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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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