Cremona's table of elliptic curves

166 = 2 · 83

Field	Data	Notes
Atkin-Lehner	2+ 83+	Signs for the Atkin-Lehner involutions
Class	166a	Isogeny class
Conductor	166	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-1328 = -1 · 24 · 83	Discriminant
Eigenvalues	2+ -1 -2  1 -5 -2 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	-30664297/1328	j-invariant
L	0.86001701545008	L(r)(E,1)/r!
Ω	4.7801672707866	Real period
R	0.089956790916707	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	1328d1 5312d1 1494d1 4150k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 166a1

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
+	-1	-2	1	-5	-2	-3	-2	4	-3	1	1	6	8	12	-14	-3	-7	2	-14	-4	-6	+	4	12

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Quadratic twists for elliptic curve 166a1

-4	8	-3	5	-7	-11	13	17	-19	-23	-83
1328d1	5312d1	1494d1	4150k1	8134a1	20086e1	28054h1	47974a1	59926g1	87814d1	13778c1

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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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