Cremona's table of elliptic curves

1066 = 2 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 13+ 41+	Signs for the Atkin-Lehner involutions
Class	1066b	Isogeny class
Conductor	1066	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-1475821568 = -1 · 214 · 133 · 41	Discriminant
Eigenvalues	2+  1 -2  2 -2 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-172,2026]	[a1,a2,a3,a4,a6]
Generators	[17:55:1]	Generators of the group modulo torsion
j	-558051585337/1475821568	j-invariant
L	2.0385244316153	L(r)(E,1)/r!
Ω	1.3347451763027	Real period
R	0.76363805908707	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	8528d1 34112e1 9594t1 26650o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1066b1

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	2	-2	+	4	0	-8	-6	7	-4	+	-6	10	-10	-13	1	10	-4	-14	4	3	13	3

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Quadratic twists for elliptic curve 1066b1

-4	8	-3	5	-7	-11	13	41
8528d1	34112e1	9594t1	26650o1	52234s1	128986bd1	13858l1	43706i1

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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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