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	28224bp	Isogeny class
Conductor	28224	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	36578304 = 210 · 36 · 72	Discriminant
Eigenvalues	2+ 3-  1 7- -1  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-252,-1512]	[a1,a2,a3,a4,a6]
Generators	[-1255:307:125]	Generators of the group modulo torsion
j	48384	j-invariant
L	6.2869169740957	L(r)(E,1)/r!
Ω	1.1997621780404	Real period
R	5.2401359945887	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	28224fj1 3528j1 3136n1 28224y1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224bp1

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
+	-	1	-	-1	2	3	5	3	-6	1	5	-10	4	1	-9	-3	3	-11	-16	-7	-11	4	-9	-6

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Quadratic twists for elliptic curve 28224bp1

-4	8	-3	-7
28224fj1	3528j1	3136n1	28224y1

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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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