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	28224gk	Isogeny class
Conductor	28224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1024192512 = -1 · 212 · 36 · 73	Discriminant
Eigenvalues	2- 3-  4 7-  0  4 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,252,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	3.7227774466902	L(r)(E,1)/r!
Ω	0.93069436167279	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28224gk2 14112ch1 3136v2 28224go2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224gk2

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	-	0	4	-8	0	0	10	0	-2	-8	0	0	14	0	12	0	0	-16	0	0	16	-8

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Quadratic twists for elliptic curve 28224gk2

-4	8	-3	-7
28224gk2	14112ch1	3136v2	28224go2

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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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