Cremona's table of elliptic curves

549 = 3² · 61

Field	Data	Notes
Atkin-Lehner	3- 61+	Signs for the Atkin-Lehner involutions
Class	549c	Isogeny class
Conductor	549	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-44469 = -1 · 36 · 61	Discriminant
Eigenvalues	1 3-  3  1  5  1 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-18,-27]	[a1,a2,a3,a4,a6]
j	-912673/61	j-invariant
L	2.3029474055306	L(r)(E,1)/r!
Ω	1.1514737027653	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	8784t1 35136bb1 61a1 13725c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 549c1

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	-	3	1	5	1	-4	-4	9	6	0	8	-5	-8	-4	-6	-9	+	-7	8	-11	3	-4	4	-14

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Quadratic twists for elliptic curve 549c1

-4	8	-3	5	-7	-11	13	61
8784t1	35136bb1	61a1	13725c1	26901v1	66429e1	92781j1	33489f1

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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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