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
Δ	-1076480 = -1 · 28 · 5 · 292	Discriminant
Eigenvalues	2-  0 5+  0 -2 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,17,-42]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	2122416/4205	j-invariant
L	1.9398167217561	L(r)(E,1)/r!
Ω	1.4398082404058	Real period
R	0.89818290487969	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	2320g2 9280e2 5220n2 2900e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 580a2

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 580a2

-4	8	-3	5	-7	-11	13	29
2320g2	9280e2	5220n2	2900e2	28420h2	70180c2	98020i2	16820a2

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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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