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	1066d	Isogeny class
Conductor	1066	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	840	Modular degree for the optimal curve
Δ	-917476352 = -1 · 210 · 13 · 413	Discriminant
Eigenvalues	2-  3  2 -2 -2 13+  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-759,-7985]	[a1,a2,a3,a4,a6]
j	-48296148523713/917476352	j-invariant
L	4.5432293313683	L(r)(E,1)/r!
Ω	0.45432293313683	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	8528f1 34112i1 9594g1 26650e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1066d1

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	2	-2	-2	+	0	0	-4	2	1	0	+	-2	-2	6	-7	13	-2	4	-10	-4	-15	-3	11

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Quadratic twists for elliptic curve 1066d1

-4	8	-3	5	-7	-11	13	41
8528f1	34112i1	9594g1	26650e1	52234bh1	128986o1	13858d1	43706x1

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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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