Cremona's table of elliptic curves

549 = 3² · 61

Field	Data	Notes
Atkin-Lehner	3+ 61+	Signs for the Atkin-Lehner involutions
Class	549a	Isogeny class
Conductor	549	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-1647 = -1 · 33 · 61	Discriminant
Eigenvalues	1 3+  0 -2 -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3,0]	[a1,a2,a3,a4,a6]
Generators	[4:6:1]	Generators of the group modulo torsion
j	91125/61	j-invariant
L	2.3235893668019	L(r)(E,1)/r!
Ω	2.9764069064814	Real period
R	1.5613385130522	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8784g1 35136e1 549b1 13725b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 549a1

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

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Quadratic twists for elliptic curve 549a1

-4	8	-3	5	-7	-11	13	61
8784g1	35136e1	549b1	13725b1	26901g1	66429b1	92781b1	33489d1

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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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