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	4	Product of Tamagawa factors cp
Δ	-23059584476866 = -1 · 2 · 714 · 17	Discriminant
Eigenvalues	2-  0 -2 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,6434,116351]	[a1,a2,a3,a4,a6]
Generators	[12498:171743:216]	Generators of the group modulo torsion
j	250404380127/196003234	j-invariant
L	3.649729104265	L(r)(E,1)/r!
Ω	0.4344298524686	Real period
R	8.4011931581723	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	13328p4 53312n3 14994bf4 41650p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666k4

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 1666k4

-4	8	-3	5	-7	17
13328p4	53312n3	14994bf4	41650p3	238c4	28322t3

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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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