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	16224b	Isogeny class
Conductor	16224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	10023699099648 = 212 · 3 · 138	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5633,-55407]	[a1,a2,a3,a4,a6]
Generators	[139:1352:1]	Generators of the group modulo torsion
j	1000000/507	j-invariant
L	4.4403341676216	L(r)(E,1)/r!
Ω	0.58143309197236	Real period
R	1.9092197489822	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	16224i2 32448cx1 48672bm2 1248g2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224b2

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	0	+	2	-2	-8	6	2	6	0	-4	8	-6	4	2	2	4	2	-12	-12	-12	18

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Quadratic twists for elliptic curve 16224b2

-4	8	-3	13
16224i2	32448cx1	48672bm2	1248g2

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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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