Cremona's table of elliptic curves

539 = 7² · 11

Field	Data	Notes
Atkin-Lehner	7- 11-	Signs for the Atkin-Lehner involutions
Class	539c	Isogeny class
Conductor	539	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-4882786447 = -1 · 79 · 112	Discriminant
Eigenvalues	1 -2  2 7- 11- -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,170,-3237]	[a1,a2,a3,a4,a6]
Generators	[123:1310:1]	Generators of the group modulo torsion
j	4657463/41503	j-invariant
L	2.0049171696895	L(r)(E,1)/r!
Ω	0.67719878289377	Real period
R	1.4803018111774	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	8624s1 34496v1 4851k1 13475i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 539c1

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

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Quadratic twists for elliptic curve 539c1

-4	8	-3	5	-7	-11	13
8624s1	34496v1	4851k1	13475i1	77c1	5929g1	91091d1

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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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