Cremona's table of elliptic curves

4560 = 2⁴ · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	4560r	Isogeny class
Conductor	4560	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-453869568000 = -1 · 218 · 36 · 53 · 19	Discriminant
Eigenvalues	2- 3+ 5- -2  0  2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-360,-32400]	[a1,a2,a3,a4,a6]
Generators	[90:810:1]	Generators of the group modulo torsion
j	-1263214441/110808000	j-invariant
L	3.232831047398	L(r)(E,1)/r!
Ω	0.41446531088181	Real period
R	1.3000006524551	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	570f1 18240cn1 13680bc1 22800cu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4560r1

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

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Quadratic twists for elliptic curve 4560r1

-4	8	-3	5	-19
570f1	18240cn1	13680bc1	22800cu1	86640ed1

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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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