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	28224eu	Isogeny class
Conductor	28224	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	193536	Modular degree for the optimal curve
Δ	-3718138366623744 = -1 · 215 · 39 · 78	Discriminant
Eigenvalues	2- 3-  3 7+  1  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-127596,17786608]	[a1,a2,a3,a4,a6]
Generators	[392:5292:1]	Generators of the group modulo torsion
j	-1668296/27	j-invariant
L	7.3180120747839	L(r)(E,1)/r!
Ω	0.44355305200615	Real period
R	0.68744238914274	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28224ev1 14112bs1 9408cn1 28224gf1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224eu1

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
-	-	3	+	1	4	-4	0	8	-7	-11	-4	4	-2	-2	-11	-7	-10	10	6	-6	-11	-11	-6	7

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Quadratic twists for elliptic curve 28224eu1

-4	8	-3	-7
28224ev1	14112bs1	9408cn1	28224gf1

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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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