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	28224ek	Isogeny class
Conductor	28224	Conductor
∏ cp	6	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	[77:567:1]	Generators of the group modulo torsion
j	-3136000/27	j-invariant
L	5.0883525162869	L(r)(E,1)/r!
Ω	0.38531604112459	Real period
R	2.200943283439	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	28224ej1 14112bp1 9408cj1 28224fe1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224ek1

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 28224ek1

-4	8	-3	-7
28224ej1	14112bp1	9408cj1	28224fe1

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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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