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	1666m	Isogeny class
Conductor	1666	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	1605658492928 = 214 · 78 · 17	Discriminant
Eigenvalues	2-  2  4 7- -6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2941,-8429]	[a1,a2,a3,a4,a6]
j	23912763841/13647872	j-invariant
L	4.9120403599749	L(r)(E,1)/r!
Ω	0.70172005142498	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	13328y1 53312bd1 14994ba1 41650o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666m1

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	4	-	-6	2	-	0	-4	8	0	4	2	-8	8	-6	4	8	-16	4	-10	-12	-12	-10	-6

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Quadratic twists for elliptic curve 1666m1

-4	8	-3	5	-7	17
13328y1	53312bd1	14994ba1	41650o1	238a1	28322bb1

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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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