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	28224gc	Isogeny class
Conductor	28224	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	36870930432 = 214 · 38 · 73	Discriminant
Eigenvalues	2- 3- -2 7- -2 -4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1596,22736]	[a1,a2,a3,a4,a6]
Generators	[-35:189:1] [-26:216:1]	Generators of the group modulo torsion
j	109744/9	j-invariant
L	7.3666773746496	L(r)(E,1)/r!
Ω	1.1291751528014	Real period
R	0.81549321161263	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28224cg2 7056bt2 9408cb2 28224fs2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224gc2

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	-	-2	-4	6	-8	-6	-10	4	-6	-6	4	-8	2	-4	-8	-8	-10	-4	-4	12	-14	-4

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Quadratic twists for elliptic curve 28224gc2

-4	8	-3	-7
28224cg2	7056bt2	9408cb2	28224fs2

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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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