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	1066c	Isogeny class
Conductor	1066	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2184	Modular degree for the optimal curve
Δ	-45829062656 = -1 · 221 · 13 · 412	Discriminant
Eigenvalues	2+ -3  1  3  6 13+  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-544,-11264]	[a1,a2,a3,a4,a6]
j	-17822531769561/45829062656	j-invariant
L	0.91964987906036	L(r)(E,1)/r!
Ω	0.45982493953018	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8528i1 34112l1 9594q1 26650p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1066c1

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	1	3	6	+	3	4	-6	4	0	-3	-	5	7	-12	6	-10	8	5	16	-10	6	14	-18

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Quadratic twists for elliptic curve 1066c1

-4	8	-3	5	-7	-11	13	41
8528i1	34112l1	9594q1	26650p1	52234n1	128986ba1	13858j1	43706o1

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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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