Cremona's table of elliptic curves

1666 = 2 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	1666i	Isogeny class
Conductor	1666	Conductor
∏ cp	39	Product of Tamagawa factors cp
deg	2184	Modular degree for the optimal curve
Δ	-802829246464 = -1 · 213 · 78 · 17	Discriminant
Eigenvalues	2-  0 -1 7+ -6  4 17-  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,407,-43095]	[a1,a2,a3,a4,a6]
Generators	[135:-1636:1]	Generators of the group modulo torsion
j	1296351/139264	j-invariant
L	3.7399730700619	L(r)(E,1)/r!
Ω	0.42410524270182	Real period
R	0.22611544430642	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	13328m1 53312k1 14994l1 41650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666i1

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
-	0	-1	+	-6	4	-	1	-3	-6	0	-3	-12	3	-10	-2	13	-10	-3	-3	-4	16	-12	1	16

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Quadratic twists for elliptic curve 1666i1

-4	8	-3	5	-7	17
13328m1	53312k1	14994l1	41650b1	1666j1	28322n1

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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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