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	28224em	Isogeny class
Conductor	28224	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	199680	Modular degree for the optimal curve
Δ	-91442045985325056 = -1 · 215 · 319 · 74	Discriminant
Eigenvalues	2- 3-  1 7+ -1  0  8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,112308,-1346128]	[a1,a2,a3,a4,a6]
Generators	[382:9864:1]	Generators of the group modulo torsion
j	2731405432/1594323	j-invariant
L	5.9850957197361	L(r)(E,1)/r!
Ω	0.19996421848427	Real period
R	3.7413541814526	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	28224el1 14112k1 9408bo1 28224fn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224em1

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	+	-1	0	8	-4	4	-5	-7	-8	-4	10	6	-1	-9	2	2	6	2	9	3	6	-1

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Quadratic twists for elliptic curve 28224em1

-4	8	-3	-7
28224el1	14112k1	9408bo1	28224fn1

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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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