Cremona's table of elliptic curves

16320 = 2⁶ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	16320ca	Isogeny class
Conductor	16320	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-163200000 = -1 · 210 · 3 · 55 · 17	Discriminant
Eigenvalues	2- 3+ 5-  1  3  2 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-25,625]	[a1,a2,a3,a4,a6]
Generators	[0:25:1]	Generators of the group modulo torsion
j	-1755904/159375	j-invariant
L	5.0374172894513	L(r)(E,1)/r!
Ω	1.4943160631556	Real period
R	0.67421041821818	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	16320bi1 4080y1 48960et1 81600iq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16320ca1

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	3	2	+	1	2	-5	-6	-1	5	4	-13	-11	4	2	8	-12	-13	-6	-4	-4	-10

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Quadratic twists for elliptic curve 16320ca1

-4	8	-3	5
16320bi1	4080y1	48960et1	81600iq1

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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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