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	28224cn	Isogeny class
Conductor	28224	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-15801827328 = -1 · 214 · 39 · 72	Discriminant
Eigenvalues	2+ 3- -2 7- -6 -3  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-336,-6496]	[a1,a2,a3,a4,a6]
Generators	[25:27:1]	Generators of the group modulo torsion
j	-7168/27	j-invariant
L	3.5411977453362	L(r)(E,1)/r!
Ω	0.51018986939319	Real period
R	1.7352352319089	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	28224ge1 3528z1 9408l1 28224bb1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224cn1

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	-	-6	-3	4	-5	4	-4	-7	9	-2	1	2	8	0	10	15	6	11	1	-6	-8	14

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Quadratic twists for elliptic curve 28224cn1

-4	8	-3	-7
28224ge1	3528z1	9408l1	28224bb1

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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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