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	1666j	Isogeny class
Conductor	1666	Conductor
∏ cp	13	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-6823936 = -1 · 213 · 72 · 17	Discriminant
Eigenvalues	2-  0  1 7- -6 -4 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,8,123]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	1296351/139264	j-invariant
L	3.9723881971751	L(r)(E,1)/r!
Ω	1.8157522584252	Real period
R	0.16828745300564	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	13328n1 53312m1 14994be1 41650s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666j1

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 1666j1

-4	8	-3	5	-7	17
13328n1	53312m1	14994be1	41650s1	1666i1	28322s1

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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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