Cremona's table of elliptic curves

32160 = 2⁵ · 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 67-	Signs for the Atkin-Lehner involutions
Class	32160w	Isogeny class
Conductor	32160	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	1809000000 = 26 · 33 · 56 · 67	Discriminant
Eigenvalues	2- 3- 5+ -2  4 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-686,-6840]	[a1,a2,a3,a4,a6]
j	558661848256/28265625	j-invariant
L	2.8070478172887	L(r)(E,1)/r!
Ω	0.93568260576245	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32160l1 64320bz1 96480s1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 32160w1

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

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Quadratic twists for elliptic curve 32160w1

-4	8	-3
32160l1	64320bz1	96480s1

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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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