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	580a	Isogeny class
Conductor	580	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	11600 = 24 · 52 · 29	Discriminant
Eigenvalues	2-  0 5+  0 -2 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8,-7]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	3538944/725	j-invariant
L	1.9398167217561	L(r)(E,1)/r!
Ω	2.8796164808116	Real period
R	0.44909145243985	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	2320g1 9280e1 5220n1 2900e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 580a1

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

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Quadratic twists for elliptic curve 580a1

-4	8	-3	5	-7	-11	13	29
2320g1	9280e1	5220n1	2900e1	28420h1	70180c1	98020i1	16820a1

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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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