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	16224n	Isogeny class
Conductor	16224	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	811919627071488 = 212 · 35 · 138	Discriminant
Eigenvalues	2- 3+  0 -2 -4 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-221953,-40150319]	[a1,a2,a3,a4,a6]
Generators	[-273:148:1] [555:2704:1]	Generators of the group modulo torsion
j	61162984000/41067	j-invariant
L	5.754424746167	L(r)(E,1)/r!
Ω	0.21996401600313	Real period
R	13.0803775334	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16224s2 32448cz1 48672m2 1248b2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224n2

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 16224n2

-4	8	-3	13
16224s2	32448cz1	48672m2	1248b2

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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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