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	16	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	[-104:486:1] [-69:676:1]	Generators of the group modulo torsion
j	1643032000/767637	j-invariant
L	5.754424746167	L(r)(E,1)/r!
Ω	0.43992803200627	Real period
R	3.27009438335	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	16224s1 32448cz2 48672m1 1248b1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224n1

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 16224n1

-4	8	-3	13
16224s1	32448cz2	48672m1	1248b1

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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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