Cremona's table of elliptic curves

3320 = 2³ · 5 · 83

Field	Data	Notes
Atkin-Lehner	2+ 5+ 83+	Signs for the Atkin-Lehner involutions
Class	3320a	Isogeny class
Conductor	3320	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-2124800 = -1 · 210 · 52 · 83	Discriminant
Eigenvalues	2+  1 5+  1  3 -4 -5  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,-80]	[a1,a2,a3,a4,a6]
Generators	[12:40:1]	Generators of the group modulo torsion
j	-470596/2075	j-invariant
L	3.826396109758	L(r)(E,1)/r!
Ω	1.0785526058796	Real period
R	0.88692848380755	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	6640b1 26560h1 29880o1 16600j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3320a1

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	+	1	3	-4	-5	0	8	-5	3	-3	-6	6	-8	4	5	-13	-10	-16	-8	10	+	-12	-2

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Quadratic twists for elliptic curve 3320a1

-4	8	-3	5
6640b1	26560h1	29880o1	16600j1

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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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