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	28224cz	Isogeny class
Conductor	28224	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-8497004544 = -1 · 217 · 33 · 74	Discriminant
Eigenvalues	2- 3+ -1 7+ -5 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-588,7056]	[a1,a2,a3,a4,a6]
Generators	[-14:-112:1] [18:48:1]	Generators of the group modulo torsion
j	-2646	j-invariant
L	7.5837102819848	L(r)(E,1)/r!
Ω	1.2285398531053	Real period
R	0.25720608706125	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28224d1 7056a1 28224cy1 28224dp1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224cz1

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
-	+	-1	+	-5	-2	-6	2	-6	-3	-5	2	-8	-4	4	9	3	12	2	-8	-14	-1	-17	-18	3

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Quadratic twists for elliptic curve 28224cz1

-4	8	-3	-7
28224d1	7056a1	28224cy1	28224dp1

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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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