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	16224w	Isogeny class
Conductor	16224	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-6230016 = -1 · 212 · 32 · 132	Discriminant
Eigenvalues	2- 3- -3  2 -2 13+ -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17,-129]	[a1,a2,a3,a4,a6]
Generators	[7:12:1]	Generators of the group modulo torsion
j	-832/9	j-invariant
L	5.1025532768739	L(r)(E,1)/r!
Ω	1.013539291124	Real period
R	0.62929889861687	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	16224p1 32448cm1 48672u1 16224k1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224w1

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
-	-	-3	2	-2	+	-3	6	6	-5	0	-1	-5	6	-6	3	-12	-7	-10	10	-11	8	14	-10	10

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Quadratic twists for elliptic curve 16224w1

-4	8	-3	13
16224p1	32448cm1	48672u1	16224k1

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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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