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	561c	Isogeny class
Conductor	561	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-15147 = -1 · 34 · 11 · 17	Discriminant
Eigenvalues	-2 3-  0 -3 11- -4 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-8,8]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-64000000/15147	j-invariant
L	1.255819114575	L(r)(E,1)/r!
Ω	3.7556570476757	Real period
R	0.083595167146068	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	8976n1 35904d1 1683i1 14025i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 561c1

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
-2	-	0	-3	-	-4	+	-2	6	-9	-4	2	-1	6	-9	13	-15	-14	-9	-14	-13	0	2	13	14

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Quadratic twists for elliptic curve 561c1

-4	8	-3	5	-7	-11	13	17
8976n1	35904d1	1683i1	14025i1	27489k1	6171h1	94809o1	9537e1

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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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