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	1066a	Isogeny class
Conductor	1066	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-472724096 = -1 · 27 · 133 · 412	Discriminant
Eigenvalues	2+  1  1 -1 -2 13+ -5  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1693,26680]	[a1,a2,a3,a4,a6]
Generators	[26:7:1]	Generators of the group modulo torsion
j	-536198730680521/472724096	j-invariant
L	2.1840344016934	L(r)(E,1)/r!
Ω	1.6515558078423	Real period
R	0.66120514708695	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	8528c1 34112d1 9594s1 26650n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1066a1

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	1	-1	-2	+	-5	0	-2	0	-8	5	+	9	-5	-4	14	10	4	-7	4	-14	-6	-2	6

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Quadratic twists for elliptic curve 1066a1

-4	8	-3	5	-7	-11	13	41
8528c1	34112d1	9594s1	26650n1	52234q1	128986bb1	13858k1	43706h1

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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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