Cremona's table of elliptic curves

28224 = 2⁶ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	28224by	Isogeny class
Conductor	28224	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	455282248974336 = 216 · 310 · 76	Discriminant
Eigenvalues	2+ 3-  2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-42924,-3265360]	[a1,a2,a3,a4,a6]
Generators	[1085:35035:1]	Generators of the group modulo torsion
j	1556068/81	j-invariant
L	6.8510283579758	L(r)(E,1)/r!
Ω	0.33275758865486	Real period
R	5.1471616212197	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28224fv3 3528l3 9408q4 576d4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224by3

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	-	4	-2	2	-4	8	6	-8	-6	-6	-4	0	-2	-4	-2	4	-8	-10	-8	4	-6	-2

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Quadratic twists for elliptic curve 28224by3

-4	8	-3	-7
28224fv3	3528l3	9408q4	576d4

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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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