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	28224dw	Isogeny class
Conductor	28224	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-432081216 = -1 · 26 · 39 · 73	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,189,0]	[a1,a2,a3,a4,a6]
Generators	[756:20790:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	4.0159181214293	L(r)(E,1)/r!
Ω	1.0000961767713	Real period
R	4.0155319205341	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	28224dw1 14112e2 28224ds1 28224dr1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224dw1

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	-	0	-4	-2	0	0	-4	0	-2	10	0	0	4	0	12	0	0	16	0	0	10	8

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Quadratic twists for elliptic curve 28224dw1

-4	8	-3	-7
28224dw1	14112e2	28224ds1	28224dr1

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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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