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	-292464640 = -1 · 211 · 5 · 134	Discriminant
Eigenvalues	2+  0 5+  0 -4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,157,-322]	[a1,a2,a3,a4,a6]
Generators	[38:246:1]	Generators of the group modulo torsion
j	208974222/142805	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	1040a4 4160d4 4680s4 2600j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 520a4

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 520a4

-4	8	-3	5	-7	-11	13
1040a4	4160d4	4680s4	2600j4	25480f3	62920q3	6760i4

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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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