Cremona's table of elliptic curves

561 = 3 · 11 · 17

Field	Data	Notes
Atkin-Lehner	3- 11- 17+	Signs for the Atkin-Lehner involutions
Class	561b	Isogeny class
Conductor	561	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-24640803 = -1 · 32 · 115 · 17	Discriminant
Eigenvalues	0 3- -2  1 11- -6 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-269,1628]	[a1,a2,a3,a4,a6]
Generators	[34:181:1]	Generators of the group modulo torsion
j	-2160697802752/24640803	j-invariant
L	1.9186947104914	L(r)(E,1)/r!
Ω	2.1348844997508	Real period
R	0.089873466724563	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	8976o1 35904e1 1683f1 14025f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 561b1

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
0	-	-2	1	-	-6	+	-6	-6	1	-8	-4	-3	8	9	-1	11	-2	11	12	7	0	-16	-5	-16

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Quadratic twists for elliptic curve 561b1

-4	8	-3	5	-7	-11	13	17
8976o1	35904e1	1683f1	14025f1	27489j1	6171f1	94809n1	9537b1

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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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