Cremona's table of elliptic curves

539 = 7² · 11

Field	Data	Notes
Atkin-Lehner	7- 11-	Signs for the Atkin-Lehner involutions
Class	539d	Isogeny class
Conductor	539	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	-18947489099 = -1 · 76 · 115	Discriminant
Eigenvalues	-2  1 -1 7- 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-506,7774]	[a1,a2,a3,a4,a6]
Generators	[44:269:1]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	1.2255668740689	L(r)(E,1)/r!
Ω	1.1027617076765	Real period
R	0.11113614714199	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8624r2 34496p2 4851l2 13475j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 539d2

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
-2	1	-1	-	-	-4	2	0	-1	0	-7	3	8	-6	-8	-6	-5	-12	-7	-3	-4	-10	6	-15	7

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Quadratic twists for elliptic curve 539d2

-4	8	-3	5	-7	-11	13
8624r2	34496p2	4851l2	13475j2	11a1	5929h2	91091f2

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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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