Cremona's table of elliptic curves

4896 = 2⁵ · 3² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Class	4896k	Isogeny class
Conductor	4896	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-1370566656 = -1 · 212 · 39 · 17	Discriminant
Eigenvalues	2- 3-  1  2 -1 -1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1272,17552]	[a1,a2,a3,a4,a6]
Generators	[16:36:1]	Generators of the group modulo torsion
j	-76225024/459	j-invariant
L	4.2160172536894	L(r)(E,1)/r!
Ω	1.5293704959793	Real period
R	0.68917526275897	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	4896m1 9792bj1 1632c1 122400bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4896k1

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	2	-1	-1	+	-1	-5	-2	2	-8	-5	5	-12	0	-2	2	4	-8	0	6	-4	-6	-2

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Quadratic twists for elliptic curve 4896k1

-4	8	-3	5	17
4896m1	9792bj1	1632c1	122400bi1	83232bf1

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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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