Cremona's table of elliptic curves

580 = 2² · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 5- 29+	Signs for the Atkin-Lehner involutions
Class	580b	Isogeny class
Conductor	580	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-116000000 = -1 · 28 · 56 · 29	Discriminant
Eigenvalues	2-  0 5- -2 -4 -6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,113,-234]	[a1,a2,a3,a4,a6]
Generators	[7:30:1]	Generators of the group modulo torsion
j	623331504/453125	j-invariant
L	2.0014236886209	L(r)(E,1)/r!
Ω	1.049460867738	Real period
R	0.42379933675103	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	2320h2 9280b2 5220l2 2900a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 580b2

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

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Quadratic twists for elliptic curve 580b2

-4	8	-3	5	-7	-11	13	29
2320h2	9280b2	5220l2	2900a2	28420a2	70180n2	98020a2	16820c2

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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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