Cremona's table of elliptic curves

16224 = 2⁵ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	16224j	Isogeny class
Conductor	16224	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-30071097298944 = -1 · 212 · 32 · 138	Discriminant
Eigenvalues	2+ 3-  2 -2  6 13+ -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5183,223055]	[a1,a2,a3,a4,a6]
j	778688/1521	j-invariant
L	3.6497883745128	L(r)(E,1)/r!
Ω	0.4562235468141	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16224o2 32448g1 48672bv2 1248i2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224j2

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

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Quadratic twists for elliptic curve 16224j2

-4	8	-3	13
16224o2	32448g1	48672bv2	1248i2

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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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