Cremona's table of elliptic curves

20160 = 2⁶ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	20160do	Isogeny class
Conductor	20160	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	16384	Modular degree for the optimal curve
Δ	-134425267200 = -1 · 210 · 37 · 52 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,312,-17512]	[a1,a2,a3,a4,a6]
Generators	[34:180:1]	Generators of the group modulo torsion
j	4499456/180075	j-invariant
L	4.3816981272538	L(r)(E,1)/r!
Ω	0.49858887871189	Real period
R	1.0985248353749	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	20160bl1 5040o1 6720bn1 100800my1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20160do1

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

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Quadratic twists for elliptic curve 20160do1

-4	8	-3	5
20160bl1	5040o1	6720bn1	100800my1

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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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