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	4896n	Isogeny class
Conductor	4896	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	793152 = 26 · 36 · 17	Discriminant
Eigenvalues	2- 3- -2  2  2  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-201,-1096]	[a1,a2,a3,a4,a6]
Generators	[17:20:1]	Generators of the group modulo torsion
j	19248832/17	j-invariant
L	3.6514124283388	L(r)(E,1)/r!
Ω	1.2680125926842	Real period
R	2.879634200327	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	4896o1 9792bn2 544b1 122400bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4896n1

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	2	2	2	+	-4	-2	-2	-10	10	-2	-4	0	-6	4	2	16	10	-6	-6	-4	-6	-14

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Quadratic twists for elliptic curve 4896n1

-4	8	-3	5	17
4896o1	9792bn2	544b1	122400bj1	83232bm1

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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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