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	28224ej	Isogeny class
Conductor	28224	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-3024568512 = -1 · 26 · 39 · 74	Discriminant
Eigenvalues	2- 3-  0 7+  2 -5  2 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1470,21854]	[a1,a2,a3,a4,a6]
Generators	[25:27:1]	Generators of the group modulo torsion
j	-3136000/27	j-invariant
L	5.2573598285738	L(r)(E,1)/r!
Ω	1.4312008338928	Real period
R	0.91834767421742	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	28224ek1 14112bq1 9408bn1 28224fd1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224ej1

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
-	-	0	+	2	-5	2	-3	-2	8	-1	5	-2	-7	8	-2	10	2	11	-12	-3	17	-16	-12	-14

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Quadratic twists for elliptic curve 28224ej1

-4	8	-3	-7
28224ek1	14112bq1	9408bn1	28224fd1

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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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