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	4560i	Isogeny class
Conductor	4560	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-1386240 = -1 · 28 · 3 · 5 · 192	Discriminant
Eigenvalues	2+ 3- 5- -2 -6  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20,60]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	-3631696/5415	j-invariant
L	4.3273821230354	L(r)(E,1)/r!
Ω	2.4288818552256	Real period
R	1.7816354936018	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	2280g1 18240by1 13680j1 22800c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4560i1

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

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Quadratic twists for elliptic curve 4560i1

-4	8	-3	5	-19
2280g1	18240by1	13680j1	22800c1	86640n1

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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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