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	1666f	Isogeny class
Conductor	1666	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-1925896 = -1 · 23 · 72 · 173	Discriminant
Eigenvalues	2+  2 -3 7-  0 -2 17-  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,31,29]	[a1,a2,a3,a4,a6]
Generators	[7:22:1]	Generators of the group modulo torsion
j	63905303/39304	j-invariant
L	2.503278590917	L(r)(E,1)/r!
Ω	1.6225472268723	Real period
R	0.514269281752	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	13328x2 53312bc2 14994cp2 41650bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666f2

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	-3	-	0	-2	-	7	-3	-6	4	-7	-6	-1	0	-6	-9	-14	5	-15	-2	-16	12	-9	-14

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Quadratic twists for elliptic curve 1666f2

-4	8	-3	5	-7	17
13328x2	53312bc2	14994cp2	41650bv2	1666b2	28322i2

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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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