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	1666c	Isogeny class
Conductor	1666	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-2739182501888 = -1 · 226 · 74 · 17	Discriminant
Eigenvalues	2+  3 -2 7+ -5 -3 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1528,83264]	[a1,a2,a3,a4,a6]
Generators	[-1392:4792:27]	Generators of the group modulo torsion
j	-164384733177/1140850688	j-invariant
L	2.9782309218072	L(r)(E,1)/r!
Ω	0.69449555281476	Real period
R	2.1441684613649	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	13328l1 53312i1 14994cb1 41650bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666c1

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
+	3	-2	+	-5	-3	+	-2	-8	-6	-4	8	6	4	-10	9	4	4	-10	-5	2	-1	-12	9	4

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Quadratic twists for elliptic curve 1666c1

-4	8	-3	5	-7	17
13328l1	53312i1	14994cb1	41650bm1	1666h1	28322c1

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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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