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	1666k	Isogeny class
Conductor	1666	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	1568025872 = 24 · 78 · 17	Discriminant
Eigenvalues	2-  0 -2 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-916,-10265]	[a1,a2,a3,a4,a6]
Generators	[-17:21:1]	Generators of the group modulo torsion
j	721734273/13328	j-invariant
L	3.649729104265	L(r)(E,1)/r!
Ω	0.8688597049372	Real period
R	2.1002982895431	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13328p1 53312n1 14994bf1 41650p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666k1

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

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Quadratic twists for elliptic curve 1666k1

-4	8	-3	5	-7	17
13328p1	53312n1	14994bf1	41650p1	238c1	28322t1

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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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