Cremona's table of elliptic curves

2820 = 2² · 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 47+	Signs for the Atkin-Lehner involutions
Class	2820b	Isogeny class
Conductor	2820	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-1184129280 = -1 · 28 · 39 · 5 · 47	Discriminant
Eigenvalues	2- 3+ 5-  1 -4  1 -7  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-62380,-5976008]	[a1,a2,a3,a4,a6]
Generators	[1842:78266:1]	Generators of the group modulo torsion
j	-104864096688707536/4625505	j-invariant
L	3.0222445144797	L(r)(E,1)/r!
Ω	0.15104544572236	Real period
R	6.6696141240274	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11280ba1 45120u1 8460f1 14100j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2820b1

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
-	+	-	1	-4	1	-7	7	-1	-1	-4	-2	-7	2	+	-7	-3	1	-2	3	2	12	-4	4	-8

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Quadratic twists for elliptic curve 2820b1

-4	8	-3	5
11280ba1	45120u1	8460f1	14100j1

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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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