Cremona's table of elliptic curves

520 = 2³ · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	520a	Isogeny class
Conductor	520	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	16640000 = 211 · 54 · 13	Discriminant
Eigenvalues	2+  0 5+  0 -4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-563,-5138]	[a1,a2,a3,a4,a6]
Generators	[338:1725:8]	Generators of the group modulo torsion
j	9636491538/8125	j-invariant
L	1.8629119108572	L(r)(E,1)/r!
Ω	0.98015427442972	Real period
R	3.8012626368254	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	1040a3 4160d3 4680s3 2600j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 520a3

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
+	0	+	0	-4	+	-6	4	0	-2	-4	-6	-6	8	0	2	4	-10	12	-4	14	-16	12	2	-2

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Quadratic twists for elliptic curve 520a3

-4	8	-3	5	-7	-11	13
1040a3	4160d3	4680s3	2600j3	25480f4	62920q4	6760i3

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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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