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	4896o	Isogeny class
Conductor	4896	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-862949376 = -1 · 212 · 36 · 172	Discriminant
Eigenvalues	2- 3- -2 -2 -2  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,1600]	[a1,a2,a3,a4,a6]
Generators	[2:36:1]	Generators of the group modulo torsion
j	-140608/289	j-invariant
L	3.1044386875619	L(r)(E,1)/r!
Ω	1.4065271812975	Real period
R	0.55179144933019	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	4896n2 9792bo1 544c2 122400be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4896o2

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 4896o2

-4	8	-3	5	17
4896n2	9792bo1	544c2	122400be2	83232bk2

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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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