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	16224r	Isogeny class
Conductor	16224	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-28427563008 = -1 · 212 · 35 · 134	Discriminant
Eigenvalues	2- 3-  0 -1 -6 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2253,41211]	[a1,a2,a3,a4,a6]
Generators	[69:468:1]	Generators of the group modulo torsion
j	-10816000/243	j-invariant
L	5.3705675684264	L(r)(E,1)/r!
Ω	1.180671507057	Real period
R	0.15162466264116	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	16224m1 32448bw1 48672k1 16224h1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224r1

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
-	-	0	-1	-6	+	2	4	-4	0	5	-6	12	7	2	12	4	11	-13	-8	1	3	-6	-6	-3

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Quadratic twists for elliptic curve 16224r1

-4	8	-3	13
16224m1	32448bw1	48672k1	16224h1

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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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