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	561d	Isogeny class
Conductor	561	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-20160657 = -1 · 34 · 114 · 17	Discriminant
Eigenvalues	-1 3-  2  0 11- -2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,68,17]	[a1,a2,a3,a4,a6]
j	34741712447/20160657	j-invariant
L	1.3001014679127	L(r)(E,1)/r!
Ω	1.3001014679127	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8976r4 35904k3 1683e4 14025e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 561d4

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	0	-	-2	-	8	-8	6	8	6	2	8	-4	6	-8	10	4	0	-10	0	12	-14	-14

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Quadratic twists for elliptic curve 561d4

-4	8	-3	5	-7	-11	13	17
8976r4	35904k3	1683e4	14025e4	27489i3	6171d4	94809q3	9537c4

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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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