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	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	561 = 3 · 11 · 17	Discriminant
Eigenvalues	-1 3-  2  0 11- -2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12,15]	[a1,a2,a3,a4,a6]
j	192100033/561	j-invariant
L	1.3001014679127	L(r)(E,1)/r!
Ω	5.2004058716507	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8976r1 35904k1 1683e1 14025e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 561d1

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 561d1

-4	8	-3	5	-7	-11	13	17
8976r1	35904k1	1683e1	14025e1	27489i1	6171d1	94809q1	9537c1

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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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