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	1666l	Isogeny class
Conductor	1666	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	2312038148 = 22 · 76 · 173	Discriminant
Eigenvalues	2-  2  0 7-  6 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5048,135925]	[a1,a2,a3,a4,a6]
j	120920208625/19652	j-invariant
L	4.2275516591671	L(r)(E,1)/r!
Ω	1.409183886389	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	13328w3 53312ba3 14994t3 41650n3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666l3

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	0	-	6	-2	-	4	0	0	4	-4	-6	8	0	-6	0	4	8	0	-2	8	0	6	-14

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Quadratic twists for elliptic curve 1666l3

-4	8	-3	5	-7	17
13328w3	53312ba3	14994t3	41650n3	34a3	28322ba3

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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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