Cremona's table of elliptic curves

3549 = 3 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	3549c	Isogeny class
Conductor	3549	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	104302515681 = 32 · 74 · 136	Discriminant
Eigenvalues	1 3-  2 7- -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8285,-290509]	[a1,a2,a3,a4,a6]
Generators	[6735:94639:27]	Generators of the group modulo torsion
j	13027640977/21609	j-invariant
L	5.3479078324333	L(r)(E,1)/r!
Ω	0.50046760777844	Real period
R	5.342911058892	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	56784bk4 10647f4 88725h4 24843d4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3549c3

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	-	-4	+	-6	-4	0	-2	0	-6	-2	-4	0	6	-12	-2	-4	0	6	-16	12	14	-18

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Quadratic twists for elliptic curve 3549c3

-4	-3	5	-7	13
56784bk4	10647f4	88725h4	24843d4	21a2

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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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