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	561a	Isogeny class
Conductor	561	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-11042163 = -1 · 310 · 11 · 17	Discriminant
Eigenvalues	0 3+ -2 -3 11-  2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3729,-86416]	[a1,a2,a3,a4,a6]
j	-5736108018368512/11042163	j-invariant
L	0.61093035433091	L(r)(E,1)/r!
Ω	0.30546517716546	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	8976ba1 35904ba1 1683g1 14025r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 561a1

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	-3	-	2	+	2	2	9	8	-12	-3	0	5	11	7	-2	3	-4	-13	8	16	15	16

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Quadratic twists for elliptic curve 561a1

-4	8	-3	5	-7	-11	13	17
8976ba1	35904ba1	1683g1	14025r1	27489u1	6171a1	94809a1	9537i1

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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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