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	28224dz	Isogeny class
Conductor	28224	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-177570054144 = -1 · 227 · 33 · 72	Discriminant
Eigenvalues	2- 3+  3 7- -3  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,84,-20272]	[a1,a2,a3,a4,a6]
Generators	[37:183:1]	Generators of the group modulo torsion
j	189/512	j-invariant
L	6.5567296482004	L(r)(E,1)/r!
Ω	0.47048165729577	Real period
R	3.4840516875233	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	28224r1 7056bj1 28224ec2 28224dd1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224dz1

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
-	+	3	-	-3	2	-6	-2	6	-9	-7	10	0	-4	12	3	3	-4	2	0	-2	-5	-9	6	13

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Quadratic twists for elliptic curve 28224dz1

-4	8	-3	-7
28224r1	7056bj1	28224ec2	28224dd1

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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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