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
deg	10752	Modular degree for the optimal curve
Δ	36143145792 = 26 · 32 · 137	Discriminant
Eigenvalues	2+ 3+  0  2  0 13+  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3098,66780]	[a1,a2,a3,a4,a6]
Generators	[-17:338:1]	Generators of the group modulo torsion
j	10648000/117	j-invariant
L	4.4403341676216	L(r)(E,1)/r!
Ω	1.1628661839447	Real period
R	0.9546098744911	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	16224i1 32448cx2 48672bm1 1248g1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 16224b1

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 16224b1

-4	8	-3	13
16224i1	32448cx2	48672bm1	1248g1

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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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