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	16224d	Isogeny class
Conductor	16224	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	4452871704720192 = 26 · 38 · 139	Discriminant
Eigenvalues	2+ 3+ -2  2 -2 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-490494,132345108]	[a1,a2,a3,a4,a6]
Generators	[398:122:1]	Generators of the group modulo torsion
j	42246001231552/14414517	j-invariant
L	3.7951557294871	L(r)(E,1)/r!
Ω	0.42754344461125	Real period
R	4.4383275867297	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	16224u1 32448bd2 48672br1 1248f1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224d1

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

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Quadratic twists for elliptic curve 16224d1

-4	8	-3	13
16224u1	32448bd2	48672br1	1248f1

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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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