Cremona's table of elliptic curves

1580 = 2² · 5 · 79

Field	Data	Notes
Atkin-Lehner	2- 5+ 79-	Signs for the Atkin-Lehner involutions
Class	1580a	Isogeny class
Conductor	1580	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	316000000 = 28 · 56 · 79	Discriminant
Eigenvalues	2-  0 5+  0  4 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-463,-3738]	[a1,a2,a3,a4,a6]
Generators	[1986:88500:1]	Generators of the group modulo torsion
j	42877229904/1234375	j-invariant
L	2.6734078587941	L(r)(E,1)/r!
Ω	1.0310234138587	Real period
R	5.1859304509653	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	6320e2 25280k2 14220g2 7900b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1580a2

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

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Quadratic twists for elliptic curve 1580a2

-4	8	-3	5	-7	-79
6320e2	25280k2	14220g2	7900b2	77420l2	124820a2

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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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