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	16224s	Isogeny class
Conductor	16224	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	237135179541312 = 26 · 310 · 137	Discriminant
Eigenvalues	2- 3-  0  2  4 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16618,356396]	[a1,a2,a3,a4,a6]
Generators	[-100:1014:1]	Generators of the group modulo torsion
j	1643032000/767637	j-invariant
L	6.7509627209754	L(r)(E,1)/r!
Ω	0.49758601301724	Real period
R	0.67837143170878	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	16224n1 32448bx2 48672l1 1248d1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224s1

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	2	4	+	-6	6	0	-2	-6	-10	-8	-12	12	-6	0	2	2	-8	-14	-4	8	-4	-14

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Quadratic twists for elliptic curve 16224s1

-4	8	-3	13
16224n1	32448bx2	48672l1	1248d1

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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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