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	28224bk	Isogeny class
Conductor	28224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-51640810647552 = -1 · 212 · 37 · 78	Discriminant
Eigenvalues	2+ 3-  0 7-  2 -2  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2940,-340256]	[a1,a2,a3,a4,a6]
Generators	[2856:29008:27]	Generators of the group modulo torsion
j	8000/147	j-invariant
L	5.6774557141641	L(r)(E,1)/r!
Ω	0.30779853637153	Real period
R	4.6113407336927	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	28224bm2 14112p1 9408ba2 4032m2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224bk2

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

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Quadratic twists for elliptic curve 28224bk2

-4	8	-3	-7
28224bm2	14112p1	9408ba2	4032m2

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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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