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	28224cu	Isogeny class
Conductor	28224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	88527103967232 = 214 · 38 · 77	Discriminant
Eigenvalues	2+ 3- -4 7-  2 -6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-64092,-6228880]	[a1,a2,a3,a4,a6]
Generators	[-152:36:1]	Generators of the group modulo torsion
j	20720464/63	j-invariant
L	3.0117753601126	L(r)(E,1)/r!
Ω	0.30010828098894	Real period
R	2.5089072435688	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	28224gp2 1764k2 9408r2 4032j2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224cu2

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
+	-	-4	-	2	-6	-4	-4	-2	-2	0	-2	0	4	12	-6	8	6	8	-14	2	12	4	0	2

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Quadratic twists for elliptic curve 28224cu2

-4	8	-3	-7
28224gp2	1764k2	9408r2	4032j2

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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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