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	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-304088967 = -1 · 32 · 7 · 136	Discriminant
Eigenvalues	1 3-  2 7- -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,165,-167]	[a1,a2,a3,a4,a6]
Generators	[445:2427:125]	Generators of the group modulo torsion
j	103823/63	j-invariant
L	5.3479078324333	L(r)(E,1)/r!
Ω	1.0009352155569	Real period
R	5.342911058892	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	56784bk1 10647f1 88725h1 24843d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3549c1

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 3549c1

-4	-3	5	-7	13
56784bk1	10647f1	88725h1	24843d1	21a4

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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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