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
Δ	-2022633897984 = -1 · 221 · 39 · 72	Discriminant
Eigenvalues	2- 3+  3 7- -3  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-53676,-4786992]	[a1,a2,a3,a4,a6]
Generators	[882705:74136411:125]	Generators of the group modulo torsion
j	-67645179/8	j-invariant
L	6.5567296482004	L(r)(E,1)/r!
Ω	0.15682721909859	Real period
R	10.45215506257	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	28224r2 7056bj2 28224ec1 28224dd2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224dz2

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 28224dz2

-4	8	-3	-7
28224r2	7056bj2	28224ec1	28224dd2

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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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