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	28224er	Isogeny class
Conductor	28224	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-1859069183311872 = -1 · 214 · 39 · 78	Discriminant
Eigenvalues	2- 3-  2 7+  6  3 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16464,-2228128]	[a1,a2,a3,a4,a6]
Generators	[366583:11886561:343]	Generators of the group modulo torsion
j	-7168/27	j-invariant
L	6.962360851824	L(r)(E,1)/r!
Ω	0.19283364511984	Real period
R	9.0263823612017	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	28224bb1 7056p1 9408br1 28224ge1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224er1

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 28224er1

-4	8	-3	-7
28224bb1	7056p1	9408br1	28224ge1

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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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